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Il'ichev, Andrej Teimurazovich

Total publications: 134 (129)
in MathSciNet: 90 (89)
in zbMATH: 54 (54)
in Web of Science: 83 (82)
in Scopus: 85 (84)
Cited articles: 78
Citations: 794
Presentations: 27

Number of views:
This page:7259
Abstract pages:11340
Full texts:2874
References:1200
Professor
Doctor of physico-mathematical sciences (1996)
Speciality: 01.02.05 (Mechanics of fluids, gases and plasmas)
Birth date: 23.05.1959
E-mail:
Website: https://www.mi.ras.ru/~ilichev
Keywords: nonlinear waves, dispersive and dissipative media, hamiltonian systems, orbital stability of bound states, solitary waves, exponential instability, Evans' function, collapse, asymptotic methods, qualitative theory of dynamical systems, center manifold reduction, normal forms.

Subject:

The scientific interests concern the propagation of nonlinear waves in dispersive and dissipative media, stability of localized wave structures and also of interfaces in fluid mechanics, elasticity, and filtration theory. A number of results were obtained about the existence and propagation of different types of solitary waves in dispersive and dissipative media of fluid mechanics. The results are included in the monography "Solitary waves in fluid dynamics". The problems are solved about the stability and instability of solitons in fluids, plasmas, elastic rods and composites and also of waveguide structures in the fluid. In a number of papers with G. G. Tsypkin a topological approach is adapted to investigation of stability of water-vapor interfaces in some models of hydrothermal systems. It was shown that stability of the interface persists for values of permeability, characteristic for natural hydrothermal reservoirs.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov State University (MSU) in 1981 (department of hydromechanics). Ph.D. thesis was defended in 1986 D.Sci. thesis was defended in 1996. A list of my works contains about 50 titles.

In 1999 I was awarded the prize named after Academician G. I. Petrov for series of papers on nonlinear problems of theory of hydrodynamical stability.

   
Main publications:
  • Haragus-Courcelle M., Ilichev A. Three dimensional solitary waves in the presence of additional surface effects // Eur. J. Mech. B/Fluids, 1998, 17, 739–768.
  • Ilichev A. Stability of solitary waves in nonlinear composite media // Physica D, 2001, 150, 264–277.

https://www.mathnet.ru/eng/person17713
List of publications on Google Scholar
https://zbmath.org/authors/ai:ilichev.andrej-t
https://mathscinet.ams.org/mathscinet/MRAuthorID/213527
https://elibrary.ru/author_items.asp?authorid=6408
https://www.webofscience.com/wos/author/record/Q-4092-2016
https://www.scopus.com/authid/detail.url?authorId=7006402366

List of publications:
| scientific publications | by years | by types | by times cited | common list |


Citations (Crossref Cited-By Service + Math-Net.Ru)

   2024
1. A. T. Il'ichev, A. S. Savin, A. Yu. Shashkov, “Motion of particles in the field of nonlinear wave packets in a liquid layer under an ice cover”, Theoret. and Math. Phys., 218:3 (2024), 503–514  mathnet  crossref  crossref  mathscinet  adsnasa  scopus
2. A. T. Il'ichev, A. S. Savin, A. Yu. Shashkov, “Motion of liquid particles in the field of 1:1 resonance nonlinear wave structures in a fluid beneath an ice cover”, Int. J. Non-Linear Mech., 160 (2024), 104665 , 9 pp.  mathnet  crossref;
3. A. T. Il'ichev, A. S. Savin, “Motion of liquid particles in the field of a surface generalized solitary wave in a fluid beneath an ice cover”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024 (to appear)  mathnet
4. Matematicheskie aspekty mekhaniki, Sbornik statei. K 60-letiyu akademika Dmitriya Valerevicha Trescheva i 70-letiyu chlena-korrespondenta RAN Sergeya Vladimirovicha Bolotina, Trudy MIAN, 327, ed. V. V. Kozlov, I. A. Taimanov, A. T. Ilichev, A. P. Chugainova, I. Yu. Polekhin, MIAN, M., 2024  mathnet
5. S. V. Bolotin, A. T. Il'ichev, V. V. Kozlov, D. V. Treschev, A. P. Chugainova, Uspekhi Mat. Nauk  mathnet  crossref

   2023
6. A. T. Il'ichev, “Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves”, Proc. Steklov Inst. Math., 322 (2023), 118–126  mathnet  crossref  crossref  scopus
7. V.I. Erofeev, A.T. Il'ichev, “Instability of supersonic solitary waves in a generalized elastic electrically conductive medium”, Contin. Mech. Thermodin., 35 (2023), 2313-2323  mathnet  crossref  mathscinet  isi
8. A.T. Ilichev, G.G. Tsypkin, “Sravnitelnyi analiz priblizhenii Darsi i Brinkmana pri perekhode k neustoichivosti v poristoi srede”, Doklady RAN. Fizika, tekhnicheskie nauki, 508:1 (2023), 30–34  crossref
9. A.T. Il'ichev, G.G. Tsypkin, “Stability of the Interface in a Porous Medium in the Framework of Darcy’s and Brinkman’s Approximations”, Transp. Porous Media, 148 (2023), 317-333  crossref 1
10. A.T. Ilichev, A.S. Savin, A.Yu. Shashkov, “Traektorii chastits zhidkosti pod ledyanym pokrovom v pole uedinennoi izgibno-gravitatsionnoi volny”, Izv. vuzov. Radiofizika, 66:10 (2023), 848-861
11. A. T. Il'ichev, A. S. Savin, A. Yu. Shashkov, Fluid Dyn., 58 (2023), 1076–1086  mathnet  crossref  crossref  isi  elib
12. Sovremennye metody mekhaniki, Sbornik statei. K 90-letiyu akademika Andreya Gennadevicha Kulikovskogo, Trudy MIAN, 322, ed. V. V. Pukhnachev, A. T. Ilichev, A. P. Chugainova, MIAN, M., 2023 , 296 pp.  mathnet
13. V. V. Pukhnachev, A. T. Il'ichev, A. P. Chugainova, “Andrei Gennad'evich Kulikovskii: On the occasion of his 90th birthday”, Proc. Steklov Inst. Math., 322 (2023), 1–3  mathnet  crossref  crossref  scopus

   2022
14. A. T. Il'ichev, V. A. Shargatov, “Stability of an aneurysm in a membrane tube filled with an ideal fluid”, Theoret. and Math. Phys., 211:2 (2022), 642–652  mathnet  crossref  crossref  mathscinet  adsnasa  scopus
15. A. T. Il'ichev, “Stability of bound states in infinite domains”, Lekts. Kursy NOC, 32, Steklov Math. Institute of RAS, Moscow, 2022, 3–58 , 58 pp.  mathnet  crossref
16. I. B. Bakholdin, A. T. Ilichev, “Fast magnetosonic solitonic structures in a quasi-neutral collision-free finite-beta plasma”, Wave Motion, 112 (2022), 102936 , 15 pp.  mathnet  crossref  mathscinet  scopus; 4
17. A. T. Il'ichev, V. A. Shargatov, “Stability of the aneurysm-type solution in a membrane tube with localized wall thinning filled with a fluid with a non-constant velocity profile”, J. Fluids Struct., 114 (2022), 103712 , 12 pp.  mathnet  crossref  mathscinet;

   2021
18. G. G. Tsypkin, A. T. Il'ichev, “Superheating of water and morphological instability of the boiling front moving in the low-permeability rock”, Int. J. Heat Mass Transfer, 167 (2021), 120820 , 8 pp.  mathnet  crossref  isi  scopus; 3
19. A. T. Il'ichev, “Effective wavelength of envelope waves on the water surface beneath an ice sheet: small amplitudes and moderate depths”, Theoret. and Math. Phys., 208:3 (2021), 1182–1200  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus
20. A. T. Il'ichev, A. S. Savin, “Evolution of perturbations of a free surface from a pulsating underwater source in a fluid of finite depth”, Fluid Dyn., 56:6 (2021), 780–785  mathnet  crossref  crossref  isi  elib  scopus

   2020
21. V. A. Shargatov, A. T. Ilichev, “Dinamika vozmuschenii pri diffuzii v poristoi srede”, Izbrannye voprosy matematiki i mekhaniki, Sbornik statei. K 70-letiyu so dnya rozhdeniya akademika Valeriya Vasilevicha Kozlova, Tr. MIAN, 310, MIAN, M., 2020, 309–321  mathnet  crossref  mathscinet  isi
22. S. V. Gorkunov, A. T. Il'ichev, V. A. Shargatov, “Critical evolution of finite perturbations of a water evaporation surface in porous media”, Fluid Dyn., 55:2 (2020), 204–212  mathnet  crossref  crossref  adsnasa  isi  elib  scopus
23. A. T. Il'ichev, “Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes”, Russian Math. Surveys, 75:5 (2020), 843–882  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
24. A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “On the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations”, J. Exp. Theor. Phys., 131:3 (2020), 481–495  mathnet  crossref  crossref  adsnasa  isi  elib  scopus
25. A. T. Il'ichev, V. A. Shargatov, Y. B. Fu, “Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube”, Acta Mech., 231 (2020), 4095–4110  mathnet  crossref  mathscinet  isi  scopus; 13
26. Vladimir A. Shargatov, Sergey V. Gorkunov, Andrej T. Il'ichev, “Stability of finite perturbations of the phase transition interface for one problem of water evaporation in a porous medium”, Appl. Math. Comput., 378 (2020), 152208 , 17 pp.  mathnet  crossref  mathscinet  isi  scopus; 1
27. G. G. Tsypkin, A. T. Il'ichev, “Comparative Analysis of the Occurrence of Water Superheating and Instability of the Boiling Front in a Porous Medium”, Dokl. Phys., 65:9 (2020), 333–337  mathnet  crossref  crossref  adsnasa  isi  elib  scopus

   2019
28. V. A. Shargatov, S. V. Gorkunov, A. T. Il'ichev, “Dynamics of front-like water evaporation phase transition interfaces”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 223–236  mathnet  crossref  mathscinet  adsnasa  isi  scopus 18
29. Andrej T. Il'ichev, Viktor Ja. Tomashpolskii, “Characteristic parameters of nonlinear surface envelope waves beneath an ice cover under pre-stress”, Wave Motion, 86 (2019), 11–20  mathnet  crossref  mathscinet  isi  scopus 8
30. A. P. Chugainova, A. T. Ilichev, V. A. Shargatov, “Stability of shock wave structures in nonlinear elastic media”, Math. Mech. Solids, 24:11 (2019), 3456-3471  mathnet  crossref  mathscinet  isi  scopus 7
31. A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spontaneously radiating shock waves”, Doklady Physics, 64:7 (2019), 293–296  mathnet  crossref  crossref  adsnasa  isi  elib  scopus
32. A. T. Il'ichev, “Physical parameters of solitary wave packets in shallow basins under ice cover”, Theoret. and Math. Phys., 201:3 (2019), 1710–1722  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus
33. A. T. Il'ichev, “Stability of solitary loops propagating along Euler's elastica”, Dynamical Processes in Generalized Continua and Structures, Adv. Struct. Mater., 103, Springer, Cham, 2019, 269–292  mathnet  crossref  mathscinet  zmath  scopus;

   2018
34. A. T. Il'ichev, S. I. Sumskoi, V. A. Shargatov, “Unsteady Flows in Deformable Pipes: The Energy Conservation Law”, Proc. Steklov Inst. Math., 300 (2018), 68–77  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
35. A. T. Il'ichev, G. G. Tsypkin, “Evolution of a Condensation Surface in a Porous Medium near the Instability Threshold”, Proc. Steklov Inst. Math., 300 (2018), 78–85  mathnet  crossref  crossref  mathscinet  mathscinet  isi  elib  scopus
36. Andrej Il'ichev, “Physical parameters of envelope solitary waves at a water-ice interface”, AIP Conf. Proc., 1982, 2018, 20036 , 6 pp.  mathnet  crossref  mathscinet  isi  scopus 2
37. A. T. Il'ichev, “Envelope solitary waves at a water-ice interface: the case of positive initial tensions”, Mathematica Montisnigri, 43 (2018), 49–57  mathnet  mathscinet  isi
38. Sovremennye problemy i metody mekhaniki, Sbornik statei. K 110-letiyu so dnya rozhdeniya akademika Leonida Ivanovicha Sedova, Trudy MIAN, 300, ed. A. G. Kulikovskii, A. T. Ilichev, A. P. Chugainova, MAIK «Nauka/Interperiodika», M., 2018 , 239 pp.  mathnet

   2017
39. Anna P. Chugainova, Andrey T. Il'ichev, Andrey G. Kulikovskii, Vladimir A. Shargatov, “Problem of arbitrary discontinuity disintegration for the generalized Hopf equation: selection conditions for a unique solution”, J. Appl. Math., 82:3 (2017), 496 , 525 pp.  mathnet  crossref  mathscinet  isi  scopus 8
40. A. T. Il'ichev, A. S. Savin, “Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column”, Theoret. and Math. Phys., 193:3 (2017), 1801–1810  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
41. A. T. Il'ichev, “Stability of solitary waves in membrane tubes: A weakly nonlinear analysis”, Theoret. and Math. Phys., 193:2 (2017), 1593–1601  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  scopus

   2016
42. A. T. Il'ichev, “Solitary wave packets beneath a compressed ice cover”, Fluid Dyn., 51:3 (2016), 327–337  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
43. G. G. Tsypkin, A. T. Il'ichev, “Dynamical instability of the evaporation front in low-permeability geothermal reservoirs”, Dokl. Phys., 61:6 (2016), 297–300  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
44. A. T. Il'ichev, A. P. Chugainova, “Spectral stability theory of heteroclinic solutions to the Korteweg–de Vries–Burgers equation with an arbitrary potential”, Proc. Steklov Inst. Math., 295 (2016), 148–157  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus
45. A. T. Il'ichev, G. G. Tsypkin, “Morphological instability of an evaporation front moving in a geothermal reservoir”, Fluid Dynamics, 51:6 (2016), 776–783  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib  scopus

   2015
46. A. T. Il'ichev, V. Ya. Tomashpolskii, “Soliton-like structures on a liquid surface under an ice cover”, Theoret. and Math. Phys., 182:2 (2015), 231–245  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
47. V. A. Shargatov, A. T. Il'ichev, G. G. Tsypkin, “Dynamics and stability of moving fronts of water evaporation in a porous medium”, Int. J. Heat and Mass Transfer, 83 (2015), 552–561  mathnet  crossref  isi  elib  scopus 26
48. A. T. Il'ichev, A. P. Chugainova, V. A. Shargatov, “Spectral stability of special discontinuities”, Dokl. Math., 91:3 (2015), 347–351  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
49. A. T. Il'ichev, “Envelope Solitary Waves and Dark Solitons at a Water–Ice Interface”, Proc. Steklov Inst. Math., 289 (2015), 152–166  mathnet  crossref  crossref  isi  elib  scopus
50. Y. B. Fu, A. T. Il'ichev, “Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow”, Math. Mech. Solids, 20 (2015), 1198–2014  mathnet  crossref  mathscinet  isi  elib  scopus 35
51. Andrej T. Il'ichev, G. G. Tsypkin, “Geothermal energy and hydrodynamic instability of phase flows”, Energy Science and Technology. Volume 9. Geothermal and Ocean Energy, eds. U. C. Sharma, R. Prasad and S. Sivakumar, Studium Press LLC, USA, Houston, 2015, 214–241  mathnet
52. A. T. Il'ichev, “Soliton-like structures on a water-ice interface”, Russian Math. Surveys, 70:6 (2015), 1051–1103  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus

   2014
53. A. T. Il'ichev, Y. B. Fu, “Stability of an inflated hyperelastic membrane tube with localized wall thinning”, Internat. J. Engrg. Sci., 80 (2014), 53–61  mathnet  crossref  mathscinet  zmath  isi  scopus 30
54. A. T. Ilichev, A. V. Krivosheev, G. G. Tsypkin, V. A. Shargatov, “Dinamika i ustoichivost dvizhuschikhsya frontov ispareniya vody v poristoi srede”, Nauchnaya sessiya NIYaU MIFI-2014, Annotatsii dokladov (Moskva, 30 iyunya – 04 iyulya 2014 g.), Natsionalnyi issledovatelskii yadernyi universitet MIFI, M., 2014, 217  elib

   2013
55. A. T. Il'ichev, G. G. Tsypkin, “Classification of the Types of Instability of Vertical Flows in Geothermal Systems”, Proc. Steklov Inst. Math., 281 (2013), 179–188  mathnet  crossref  crossref  mathscinet  isi  elib
56. A. T. Il'ichev, V. A. Shargatov, “Dynamics of vater evaporation fronts”, Comput. Math. Math. Phys., 53:9 (2013), 1350–1370  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
57. A. T. Ilichev, A. A. Savin, “Defocusing of nonlinear wave packets on an ice cover”, Engineering Journal: Science and Innovation, 2013, no. 2, 47–25  mathnet  crossref  elib
58. A. T. Ilichev, G. G. Tsypkin, “Interaction of stabilizing and destabilizing factors and bifurcations of phase transition fronts”, Engineering Journal: Science and Innovation, 2013, no. 2, 44–13  mathnet  crossref  elib
59. A. T. Il'ichev, V. V. Kozlov, D. V. Trechshev, A. P. Chugainova, “Andrei Gennad'evich Kulikovskii (on his 80th birthday)”, Russian Math. Surveys, 68:6 (2013), 1145–1155  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib

   2012
60. A. T. Il'ichev, V. Ja. Tomashpolskii, “Instability of solitons under flexure and twist of an elastic rod”, Theoret. and Math. Phys., 172:3 (2012), 1206–1216  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
61. A. T. Il'ichev, Y.-B. Fu, “Stability of aneurysm solutions in a fluid-filled elastic membrane tube”, Acta Mechanica Sinica, 28:4 (2012), 1209–1218  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus 31
62. A. T. Il'ichev, A. A. Savin, A. S. Savin, “Formation of wave on an ice-sheet above the dipole, moving in a fluid”, Dokl. Phys., 57:5 (2012), 202–205  mathnet  crossref  mathscinet  adsnasa  isi  elib  scopus
63. A. T. Il'ichev, G. G. Tsypkin, “Stability of water-vapor phase transition in geothermal systems”, Fluid Dynamics, 47:4 (2012), 501–510  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus

   2011
64. A. T. Il'ichev, G. G. Tsypkin, “Influence of advective transfer of energy on stability water over steam in geothermal reservoirs”, Dokl. Phys., 56 (2011), 227–231  crossref  adsnasa  isi  elib  scopus

   2010
65. Y. B. Fu, A. T. Il'ichev, “Solitary waves in fluid-filled elastic tubes: existence, persistence, and the role of axial displacement”, IMA J. Appl. Math., 75:2 (2010), 257–268  crossref  mathscinet  zmath  isi  elib  scopus 30

   2009
66. A. T. Ilichev, Ustoichivost lokalizovannykh voln v nelineino-uprugikh sterzhnyakh, Fizmatlit, M., 2009 , 159 pp.

   2008
67. A. T. Il'ichev, G. G. Tsypkin, D. Pritchard, Ch. N. Richardson, “Instability of the salinity profile during the evaporation of saline groundwater”, J. Fluid Mech., 614 (2008), 87–104  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus 29
68. A. T. Il'ichev, “Neutral stability of compression solitons in the bending of a nonlinearly elastic rod”, J. Appl. Math. Mech., 72:3 (2008), 323–330  crossref  mathscinet  zmath  isi  elib  scopus
69. A. Il'ichev, G. Tsypkin, “Long-wave transition to instability of flows in horizontally extended domains of porous media”, IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, IUTAM Bookser., 6, Springer-Verlag, Dordrecht, 2008, 291–301  crossref  mathscinet  zmath  isi  scopus
70. A. T. Il'ichev, G. G. Tsypkin, “Catastrophic transition to instability of evaporation front in a porous medium”, Eur. J. Mech. B Fluids, 27:6 (2008), 665–677  crossref  mathscinet  zmath  isi  elib  scopus 28
71. A. T. Il'ichev, V. E. Odintsova,, “Evolution of a long-wave train in loss of stability of a phase interface in geothermal systems”, Fluid Dyn., 43:1 (2008), 97–104  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
72. A. T. Il'ichev, G. G. Tsypkin, “Instabilities of uniform filtration flows with phase transition”, J. Exp. Theor. Phys., 107:4 (2008), 699–711  crossref  adsnasa  isi  elib  elib  scopus

   2007
73. A. T. Il'ichev, G. G. Tsypkin, “Rayleigh–Taylor instability of an interface in a nonwettable porous medium”, Fluid Dynam., 42:1 (2007), 83–90  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
74. A. T. Ilichev, G. G. Tsypkin, “Slabonelineinaya teoriya neustoichivosti dlinnovolnovykh vozmuschenii”, Dokl. RAN, 416:2 (2007), 192–194  mathnet  zmath  elib 3

   2006
75. G. G. Tsypkin, A. T. Il'ichev, “Rigid transition to the Rayleigh-Taylor instability of interface in a porous medium”, Dokl. Phys., 51:9 (2006), 523–527  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
76. A. T. Il'ichev, “Instability of solitary waves on Euler's elastica”, Z. Angew. Math. Phys., 57:4 (2006), 547–566  crossref  mathscinet  zmath  isi  scopus 8
77. L . Brevdo, A. Il'ichev, “Uni-modal destabilization of a visco-elastic floating ice layer by wind stress”, Eur. J. Mech. A Solids, 25:3 (2006), 509–525  crossref  mathscinet  zmath  isi  elib  scopus 4

   2005
78. A. T. Il'ichev, G. G. Tsypkin, “Transition to instability of the interface in geothermal systems”, Eur. J. Mech. B Fluids, 24:4 (2005), 491–501  crossref  mathscinet  zmath  isi  elib  scopus 14
79. A. T. Il'ichev, “Stability Theory of the Euler Loop on Inextensible Elastic Rods”, Proc. Steklov Inst. Math., 251 (2005), 146–164  mathnet  mathscinet  zmath

   2004
80. A. T. Ilichev, “Neustoichivost solitonov v nerastyazhimykh sterzhnyakh”, Dokl. RAN, 397:3 (2004), 304–307  mathnet  mathscinet  zmath 1
81. A. T. Il'ichev, G. G. Tsypkin, “Criteria of hydrodynamic instability of a phase interface in hydrothermal systems”, Fluid Dynam., 39:5 (2004), 762–770  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
82. A. T. Il'ichev, A. S. Savin, “On the process of establishment of surface waves in plane flow”, Fluid Dynam., 39:4 (2004), 574–581  crossref  mathscinet  zmath  adsnasa  isi  scopus
83. L. Brevdo, A. Il'ichev, “Absolute instability of a thin visco-elastic plate in an air flow”, Eur. J. Mech. A Solids, 23:6 (2004), 1069–1084  crossref  mathscinet  zmath  isi  elib  scopus 4
84. G. Tsypkin, A. Il'ichev, “Gravitational stability of the interface in water over steam geothermal reservoirs”, Transp. Porous Media, 55:2 (2004), 183–199  crossref  mathscinet  isi  elib  scopus 33
85. A. T. Ilichev, G. G. Tsypkin, “Kriterii gidrodinamicheskoi ustoichivosti sloya tyazheloi zhidkosti nad legkoi v geotermalnom rezervuare”, Dokl. RAN, 396:5 (2004), 615–619  mathnet

   2003
86. I. Bakholdin, A. Il'ichev, “Instability and collapse of waveguides on the water surface under the ice cover”, Eur. J. Mech. B Fluids, 22:3 (2003), 291–304  crossref  mathscinet  zmath  isi  elib  scopus 4
87. A. T. Ilichev, Uedinennye volny v modelyakh gidromekhaniki, Fizmatlit, 2003 , 256 pp.

   2002
88. A. T. Il'ichev, “Instability of waveguides in a liquid with surface effects”, Fluid Dynam., 37:6 (2002), 919–930  crossref  mathscinet  zmath  isi  elib  scopus
89. A. T. Il'ichev, G. G. Tsypkin, “Gravitational stability of a moving water-steam interface in hydrothermal systems”, Fluid Dynam., 37:1 (2002), 3–12  mathscinet  zmath  elib
90. I. Bakholdin, A. Il'ichev, V. Tomashpol'skii, “Stability, instability and interaction of solitary pulses in a composite medium”, Eur. J. Mech. A Solids, 21:2 (2002), 333–346  crossref  mathscinet  zmath  isi  elib  scopus 3
91. I. Bakholdin, A. Il'ichev, A. Zharkov, “Steady magnetoacoustic waves and decay of solitonic structures in a finite-beta plasma”, J. Plasma Physics, 67 (2002), 1–26  crossref  adsnasa  isi  elib  scopus 5

   2001
92. I. B. Bakholdin, A. T. Il'ichev, “Instability of solitary waves in non-linear composite media”, J. Appl. Math. Mech., 65:6 (2001), 977–984 (2002)  crossref  mathscinet  zmath  isi  elib  scopus
93. F. Dias, A. Il'ichev, “Interfacial waves with free-surface boundary conditions: an approach via a model equation”, Phys. D, 150:3-4 (2001), 278–300  crossref  mathscinet  zmath  isi  elib  scopus 17
94. A. Il'ichev, “Stability of solitary waves in nonlinear composite media”, Phys. D, 150:3-4 (2001), 264–277  crossref  mathscinet  zmath  isi  elib  scopus 8
95. L. Brevdo, F. Il'ichev, “Multi-modal destabilization of a floating ice layer by wind stress”, Cold Reg. Sci. Technol., 33 (2001), 77–89  crossref  elib  scopus 8
96. G. G. Tsypkin, A. T. Ilichev, “Ustoichivost statsionarnogo fronta fazovykh perekhodov voda-par v gidrotermalnykh sistemakh”, Dokl. RAN, 378 (2001), 197–200  mathnet 1

   2000
97. A. A. Zharkov, A. T. Il'ichev, “Solitary waves in a collisionless plasma with isothermal pressure”, Fluid Dynam., 35:5 (2000), 738–747  crossref  mathscinet  zmath  elib
98. A. T. Il'ichev, “Solitary waves in media with dispersion and dissipation (a review)”, Fluid Dynam., 35:2 (2000), 157–176  crossref  mathscinet  zmath  adsnasa  elib  scopus
99. I. B. Bakholdin, F. F. Zharkov, A. N. Il'ichev, “Decay of solitons in an isotropiic collisionless quasineutral plasma with isothermal pressure”, J. Exp. Theor. Phys, 2000, 111–125  crossref  adsnasa  scopus
100. A. T Ilichev, “Ustoichivost solitonov v nelineinykh kompozitnykh sredakh”, ZhETF, 118 (2000), 720–729

   1999
101. A. Il'ichev, “Self-channelling of surface water waves in the presence of an additional surface pressure”, Three-dimensional aspects of air-sea interaction (Nice, 1998), Eur. J. Mech. B Fluids, 18, no. 3, 1999, 501–510  crossref  mathscinet  zmath  isi  elib  scopus 7
102. I. Bakholdin, A. Il'ichev, “Solitary wave decay in non-linear Faraday resonance”, Eur. J. Mech. B Fluids, 18:1 (1999), 93–102  crossref  mathscinet  zmath  isi  elib  scopus 1

   1998
103. I. Bakholdin, A. Il'ichev, “Solitary wave instability in a cold plasma”, Proceedings of the IX International Conference on Waves and Stability in Continuous Media (Bari, 1997), Rend. Circ. Mat. Palermo (2) Suppl., no. 57, 1998, 33–38  mathscinet  zmath
104. M. Hărăguş-Courcelle, A. Il'ichev, “Three-dimensional solitary waves in the presence of additional surface effects”, Eur. J. Mech. B Fluids, 17:5 (1998), 739–768  crossref  mathscinet  zmath  isi  elib  scopus 33
105. A. Il'ichev, “Faraday resonance: asymptotic theory of surface waves”, Phys. D, 119:3-4 (1998), 327–351  crossref  mathscinet  zmath  isi  elib  scopus 4
106. L. Brevdo, A. Il'ichev, “Exponential neutral stability of a floating ice layer”, Z. Angew. Math. Phys., 49:3 (1998), 401–419  crossref  mathscinet  zmath  isi  scopus 6
107. I. Bakholdin, A. Il'ichev, “Solitary-wave decay in a cold plasma”, J. Plasma Physics, 60 (1998), 569–580  crossref  mathscinet  adsnasa  isi  scopus 9

   1997
108. A. T. Il'ichev, “Solitary and generalized solitary waves in dispersive media”, J. Appl. Math. Mech., 61:4 (1997), 587–600  crossref  mathscinet  zmath  isi  scopus
109. A. T. Il'ichev, A. V. Marchenko, “The formation of non-linear waveguides in the resonant interaction of three surface waves”, J. Appl. Math. Mech., 61:2 (1997), 183–193  crossref  mathscinet  zmath  isi  scopus

   1996
110. I. Bakholdin, A. Il'ichev, “Radiation and modulational instability described by the fifth-order Korteweg-de Vries equation”, Mathematical problems in the theory of water waves (Luminy, 1995), Contemp. Math., 200, Amer. Math. Soc., Providence, RI, 1996, 1–15  crossref  mathscinet  zmath 13
111. A. Beliaev, A. Il'ichev, “Conditional stability of solitary waves propagating in elastic rods”, Phys. D, 90:1-2 (1996), 107–118  crossref  mathscinet  zmath  isi  elib  scopus 12
112. A. T. Il'ichev, “Solitary waves in a cold plasma”, Math. Notes, 59:5 (1996), 518–524  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
113. A. T. Ilichev, “Uedinennye volny-pakety v kholodnoi plazme”, Izv. RAN. MZhG, 1996, no. 5, 154–161  zmath
114. A. T. Il'ichev, “Steady waves in a cold plasma”, J. Plasma Physics, 55 (1996), 181–194  crossref  adsnasa  isi  scopus 15

   1995
115. A. T. Il'ichev, “Periodic and quasi-periodic Alfvenic structures in a cold plasma”, Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids (Hannover, 1994), Adv. Ser. Nonlinear Dynam., 7, World Sci. Publ., River Edge, NJ, 1995, 275–281  mathscinet  zmath
116. A. T. Il'ichev, A. V. Marchenko, “Nonlinear waveguides in resonance three-wave interaction in an ideal fluid with surface effects”, BRAS Physics/Supplement Physics of Vibrations, 59:2 (1995), 98–107
117. A. T. Il'ichev, “The existence of solitary waves in dispersive media”, BRAS Physics/Supplement Physics of Vibrations, 59:2 (1995), 88–97
118. A. T. Il'ichev, “On the existence of generalized solitary waves in media with weak dispersion”, BRAS Physics/Supplement Physics of Vibrations, 59:3 (1995), 130–140

   1992
119. A. T. Il'ichev, “Existence of a family of soliton-like solutions for the Kawahara equation”, Math. Notes, 52:1 (1992), 662–668  mathnet  crossref  mathscinet  zmath  isi  scopus
120. A. T. Il'ichev, A. Yu. Semenov, “Stability of solitary waves in dispersive media described by a fifth-order evolution equation”, Theoretical and Computational Fluid Dynamics, 3 (1992), 307-326  crossref  zmath  adsnasa  scopus 47

   1991
121. A. T. Il'ichev, A. Yu. Semenov, “Orbital stability of boundary states in the theory of long waves with additional pressure”, Soviet Phys. Dokl., 36:11 (1991), 761–762 (1992)  mathnet  mathscinet  zmath  adsnasa  isi
122. A. T. Il'ichev, A. Yu. Semënov, Stability of subcritical solitary wave solutions to fifth order evolution equation, Preprint № 28, Akad. Nauk SSSR Inst. Obshcheĭ Fiz., Moscow, 1991 , 44 pp.  mathscinet  zmath

   1990
123. A. T. Il'ichev, “Theory of nonlinear waves described by fifth-order evolution equations”, Fluid Dynam., 25:2 (1990), 247–252  crossref  mathscinet  adsnasa  scopus

   1989
124. A. T. Il'ichev, A. V. Marchenko, “Propagation of long nonlinear waves in a ponderable fluid beneath an ice sheet”, Fluid Dynam., 24:1 (1989), 73–79  crossref  mathscinet  zmath  adsnasa  scopus
125. V. P. Korobeĭnikov, A. T. Il'ichev, “On some methods of qualitative investigation of one-dimensional evolution equations in continuum mechanics”, Nonlinear wave motion, Pitman Monogr. Surveys Pure Appl. Math., 43, Longman Sci. Tech., Harlow, 1989, 129–147  mathscinet

   1991
126. A. T. Il'ichev, “Properties of a fifth-order nonlinear evolution equation that describes wave processes in media with weak dispersion”, Proc. Steklov Inst. Math., 186 (1991), 255–260  mathnet  mathscinet  zmath

   1987
127. N. R. Sibgatullin, A. T. Ilichev, “A new method for the integration of equations for axisymmetric and stationary electrovacuum fields and the construction of their general solution”, Gravitatsiya i teoriya otnositelnosti, 24, 1987, 80–93  mathscinet
128. A. T. Ilichev, V. P. Korobeinikov, “Evolution of singular perturbations in nonlinear media with weak dispersion”, Proceedings of the Eleventh International Conference on Nonlinear Oscillations (Budapest, 1987), János Bolyai Math. Soc., Budapest, 1987, 290–292 (Russian)  mathscinet

   1986
129. A. T. Ilichev, “The Sturm-Liouville problem for stationary axisymmetric gravitational fields”, Dokl. AN SSSR, 291:1 (1986), 67–71  mathnet  mathscinet  adsnasa  isi
130. A. T. Ilichev, N. R. Sibgatullin, “Effektivnoe postroenie topologicheski netrivialnykh reshenii v OTO”, Izvestiya vuzov MV i SSO SSSR, Fizika, 1986, no. 9, 75–81

   1985
131. A. T. Ilichev, N. R. Sibgatullin, “Mathematical construction of multivalent solutions in general relativity theory”, Dokl. AN SSSR, 282:5 (1985), 1098–1103  mathnet  mathscinet  adsnasa  isi
132. A. T. Ilichev, N. R. Sibgatullin, “Some solutions of supergravity equations on the background of a cosmological model”, Vestn. Mosk. un-ta. Ser. 1 Matem. Mekh., 1985, no. 1, 83–86  mathnet  mathscinet  mathscinet  adsnasa  isi

   1984
133. A. T. Ilichev, “Static soliton solutions of Einstein-Maxwell equations”, Dokl. AN SSSR, 278:1 (1984), 82–85  mathnet  mathscinet  adsnasa  isi
134. A. T. Il'ichev, “Static soliton solutions of Einstein–Maxwell equations”, Dokl. Akad. Nauk SSSR, 278:1 (1984), 82–85  mathnet  mathscinet  adsnasa

Presentations in Math-Net.Ru
1. Спектральная неустойчивость сверхзвуковых уединенных волн в упругой проводящей микрополярной среде
A. T. Il'ichev

December 12, 2024 13:00
2. Motion of particles in the field of nonlinear wave packets and dark solitons in a fluid beneath an ice cover
A. T. Il'ichev
Dynamics days in Sirius. On the occasion of academician Dmitry V. Treschev’s anniversary
October 28, 2024 11:20
3. Динамические системы и поток на центральном многообразии: приложение к теории нелинейных волн в диспергирующих средах
A. T. Il'ichev
School of Young Mechanics and Mathematicians SYMM 2024
October 7, 2024 14:15   
4. Траектории жидких частиц в поле нелинейного волнового пакета и темного солитона в жидкости под ледяным покровом
A. T. Il'ichev
Seminar of the Department of Mechanics
October 23, 2023 12:00
5. Траектории частиц жидкости в поле поверхностной уединенной волны в слое жидкости под ледяным покровом
A. T. Il'ichev, A. S. Savin, А. Ю. Шашков
International Conference "Mathematical Methods of Mechanics" dedicated to the anniversary of academician A. G. Kulikovskii
March 21, 2023 12:00   
6. Введение в мини-курс «Методы получения и исследования решений нелинейных уравнений в частных производных» + Нелинейные волновые процессы в диспергирующих средах: уравнение Кортевега-де Фриза и свойства его решений
A. T. Il'ichev
School of Young Mechanics and Mathematicians SYMM 2022
October 3, 2022 15:00   
7. Stability of the aneurism in a membrane tube with localized wall thinning filled with a fluid having a non-constant velocity profile
A. T. Il'ichev, V. A. Shargatov
International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko
June 9, 2022 12:30   
8. Stability of the aneurysm in a membrane tube with localized wall thinning filled with a fluid with a non-constant velocity profile
A. T. Il'ichev
Beijing–Moscow Mathematics Colloquium
May 13, 2022 12:00
9. Characteristic and dynamic stability of nonlinear solitary strain waves in a liquid-filled elastic membrane tube
A. T. Il'ichev
School of Young Scientists "Mathematical Methods of Mechanics"
November 2, 2021 11:00   
10. Характеристика и динамическая устойчивость нелинейных уединенных волн деформации в заполненной жидкостью упругой мембранной трубке
A. T. Il'ichev
Seminar of the Department of Mechanics
June 15, 2021 16:00   
11. Lecture 12. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
December 2, 2020 18:00   
12. Lecture 11. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
November 25, 2020 18:00   
13. Lecture 10. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
November 18, 2020 18:00   
14. Lecture 9. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
November 11, 2020 18:00   
15. Lecture 8. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
October 28, 2020 18:00   
16. Lecture 7. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
October 21, 2020 18:00   
17. Lecture 6. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
October 14, 2020 18:00   
18. Lecture 5. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
October 7, 2020 18:00   
19. Lecture 4. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
September 30, 2020 18:00   
20. Lecture 3. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
September 23, 2020 18:00   
21. Lecture 2. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
September 16, 2020 18:00   
22. Lecture 1. Stability of non-uniform states in unbounded spatial domains
A. T. Il'ichev
Course by A. T. Il'ichev "Stability of non-uniform states in unbounded spatial domains"
September 9, 2020 18:00   
23. Dynamics of front-like water evaporation phase transition interfaces
A. T. Il'ichev
Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2019
November 20, 2019 15:45   
24. Волновые структуры на поверхности раздела вода-лед
A. T. Il'ichev
Seminar of the Department of Mechanics
May 21, 2018 12:00
25. Динамика фронтов испарения воды
A. T. Il'ichev
Scientific session of the Steklov Mathematical Institute dedicated to the results of 2013
November 20, 2013 14:40   
26. Solitons in elastic shells
A. T. Il'ichev
Steklov Mathematical Institute Seminar
January 28, 2010 16:00   
27. Stability of solitons in elastic composite media
A. T. Il'ichev
Steklov Mathematical Institute Seminar
May 17, 2001

Books in Math-Net.Ru
  1. Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, ed. V. V. Kozlov, I. A. Taimanov, A. T. Il'ichev, A. P. Chugainova, I. Yu. Polekhin, 2024
    http://mi.mathnet.ru/book2006
  2. Modern Methods of Mechanics, Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii, Trudy Mat. Inst. Steklova, 322, ed. V. V. Pukhnachev, A. T. Il'ichev, A. P. Chugainova, 2023, 296 с.
    http://mi.mathnet.ru/book1947
  3. A. T. Il'ichev, Stability of bound states in infinite domains, Lekts. Kursy NOC, 32, 2022, 58 с.
    http://mi.mathnet.ru/book1914
  4. Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, ed. A. G. Kulikovskii, A. T. Il'ichev, A. P. Chugainova, 2018, 239 с.
    http://mi.mathnet.ru/book1686

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