General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

UFN, 1997, Volume 167, Number 4, Pages 377–406 (Mi ufn1303)  

This article is cited in 80 scientific papers (total in 80 papers)


Solitons and their interactions in classical field theory

T. I. Belova, A. E. Kudryavtsev

State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow

Abstract: Effects of nonlinearity in the classical field theory for non-integrable systems are considered, such as soliton scattering, soliton bound states, the fractal nature of resonant structures, kink scattering by inhomogeneities, and bubble collapse. The results are presented in both (1 + 1) and higher dimensions. Both neutral and charged scalar fields are considered. Possible application areas for the nonlinearity effects are discussed.


Full text: PDF file (5285 kB)
Full text:

English version:
Physics–Uspekhi, 1997, 40:4, 359–386

Bibliographic databases:

PACS: 03.50.-z, 03.50.Kk, 52.35.Py, 52.35.Sb
Received: March 1, 1997

Citation: T. I. Belova, A. E. Kudryavtsev, “Solitons and their interactions in classical field theory”, UFN, 167:4 (1997), 377–406; Phys. Usp., 40:4 (1997), 359–386

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O.M.. Braun, Yu.S.. Kivshar, “Nonlinear dynamics of the Frenkel–Kontorova model”, Physics Reports, 306:1-2 (1998), 1  crossref  isi  scopus
    2. Gani V., Kudryavtsev A., “Kink-Antikink Interactions in the Double sine-Gordon Equation and the Problem of Resonance Frequencies”, Phys. Rev. E, 60:3 (1999), 3305–3309  crossref  adsnasa  isi  scopus
    3. Gani V., Kudryavtsev A., Belova T., “Decay of a Bubble of Disoriented Chiral Condensate”, Phys. Atom. Nuclei, 62:5 (1999), 895–899  adsnasa  isi
    4. Obrant G., Ryskin M., “Multipion Coherent Effects in High Energy Heavy-Ion Collisions”, Phys. Rev. C, 62:2 (2000), 024903  crossref  adsnasa  isi  scopus
    5. Dyshko A., Konyukhova N., Voronov N., “Automodelling Solutions of the Higgs-Field Nonlinear Wave Equation in the de Sitter Space”, Comput. Phys. Commun., 126:1-2 (2000), 57–62  crossref  zmath  adsnasa  isi  scopus
    6. Galiev S., “Unfamiliar Waves Excited Due to Parametric and Resonant Effects”, Unsolved Problems of Noise and Fluctuations, AIP Conference Proceedings, 511, eds. Abbott D., Kish L., Amer Inst Physics, 2000, 361–367  crossref  adsnasa  isi
    7. A. L. Duischko, N. B. Konyukhova, “Multiple one-dimensional and spherically symmetric self-similar solutions to the nonlinear wave equation for the Higgs field in the de Sitter space”, Comput. Math. Math. Phys., 41:3 (2001), 435–456  mathnet  mathscinet  zmath
    8. Galiev S., Galiyev TS., “Nonlinear Trans-Resonant Waves, Vortices and Patterns: From Microresonators to the Early Universe”, Chaos, 11:3 (2001), 686–704  crossref  zmath  adsnasa  isi  scopus
    9. Belova T., Gani V., Kudryavtsev A., “Decay of a Large-Amplitude Bubble of a Disoriented Chiral Condensate”, Phys. Atom. Nuclei, 64:1 (2001), 140–142  crossref  adsnasa  isi  scopus
    10. A. L. Duischko, N. B. Konyukhova, “Multiple self-similar string and monopole solutions to nonlinear wave equations in inflationary cosmology”, Comput. Math. Math. Phys., 42:4 (2002), 450–469  mathnet  mathscinet  zmath
    11. Kevrekidis P., Dmitriev S., Takeno S., Bishop A., Aifantis E., “Rich Example of Geometrically Induced Nonlinearity: From Rotobreathers and Kinks to Moving Localized Modes and Resonant Energy Transfer”, Phys. Rev. E, 70:6, Part 2 (2004), 066627  crossref  mathscinet  adsnasa  isi
    12. Zav'yalov D., Kaplya E., Kryuchkov S., “The Dynamics of Electromagnetic Solitons Near a Semiconductor Superlattice Discontinuity”, Laser Phys., 14:10 (2004), 1310–1313  isi
    13. Koutvitsky V., Maslov E., “Parametric Instability of the Real Scalar Pulsons”, Phys. Lett. A, 336:1 (2005), 31–36  crossref  zmath  adsnasa  isi  elib  scopus
    14. Dzedolik I., “Three-Dimensional Solitary Waves in Dielectric Medium”, Caol 2005: Proceedings of the 2nd International Conference on Advanced Optoelectronics and Lasers, Vol 2, ed. Sukhoivanov I., IEEE, 2005, 148–152  crossref  isi  scopus
    15. M. A. Knyazev, “Kink with Allowance for the Energy Dissipation and Pumping”, Russ Phys J, 48:5 (2005), 483  crossref  scopus
    16. Dmitriev S.V., Kevrekidis P.G., Yoshikawa N., Frantzeskakis D.J., “Exact Static Solutions for Discrete Phi(4) Models Free of the Peierls-Nabarro Barrier: Discretized First-Integral Approach”, Phys. Rev. E, 74:4, Part 2 (2006), 046609  crossref  mathscinet  adsnasa  isi  elib  scopus
    17. Dzedolik I.V., “Spontaneous Symmetry Breaking in an Electromagnetic Field-Insulator System”, Tech. Phys., 51:7 (2006), 932–937  crossref  isi  scopus
    18. Dmitriev S.V., Kevrekidis P.G., Yoshikawa N., “Standard Nearest-Neighbour Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum”, J. Phys. A-Math. Gen., 39:23 (2006), 7217–7226  crossref  zmath  adsnasa  isi  elib  scopus
    19. Koutvitsky V., Maslov E., “Instability of Coherent States of a Real Scalar Field”, J. Math. Phys., 47:2 (2006), 022302  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. Roy I., Dmitriev S.V., Kevrekidis P.G., Saxena A., “Comparative Study of Different Discretizations of the Phi(4) Model”, Phys. Rev. E, 76:2, Part 2 (2007), 026601  crossref  mathscinet  adsnasa  isi  elib  scopus
    21. Linhares C.A., de Oliveira H.P., “Galerkin-Method Approach to Nonlinear Soliton Classical Stability”, Braz. J. Phys., 37:2A (2007), 368–377  crossref  mathscinet  adsnasa  isi  elib  scopus
    22. Busch K., von Freymann G., Linden S., Mingaleev S.F., Tkeshelashvili L., Wegener M., “Periodic Nanostructures for Photonics”, Phys. Rep.-Rev. Sec. Phys. Lett., 444:3-6 (2007), 101–202  crossref  adsnasa  isi  scopus
    23. Loginov A.Yu., “Nontopological Soliton Configuration in System Involving Three Interacting Scalar Fields and Obeying Global U(1) X U(1) Symmetry”, Phys. Atom. Nuclei, 70:5 (2007), 945–959  crossref  adsnasa  isi  elib  scopus
    24. Kevrekidis P.G., Khare A., Saxena A., Bena I., Bishop A.R., “Asymptotic Calculation of Discrete Non-Linear Wave Interactions”, Math. Comput. Simul., 74:4-5 (2007), 405–413  crossref  zmath  isi  scopus
    25. Zhu Y., Yang J., “Universal Fractal Structures in the Weak Interaction of Solitary Waves in Generalized Nonlinear Schrodinger Equations”, Phys. Rev. E, 75:3, Part 2 (2007), 036605  crossref  mathscinet  adsnasa  isi  elib  scopus
    26. Puzynin I.V., Boyadzhiev T.L., Vinitskii S.I., Zemlyanaya E.V., Puzynina T.P., Chuluunbaatar O., “Methods of Computational Physics for Investigation of Models of Complex Physical Systems”, Phys. Part. Nuclei, 38:1 (2007), 70–116  crossref  adsnasa  isi  elib  scopus
    27. A. Ludu, P.G. Kevrekidis, “Nonlinear dispersion relations”, Mathematics and Computers in Simulation, 74:2-3 (2007), 229  crossref  mathscinet  zmath  isi  scopus
    28. Dmitriev S.V., Kevrekidis P.G., Kivshar Yu.S., “Radiationless Energy Exchange in Three-Soliton Collisions”, Phys. Rev. E, 78:4, Part 2 (2008), 046604  crossref  mathscinet  adsnasa  isi  elib  scopus
    29. M. M. Bogdan, O. V. Charkina, “Dynamics of bound soliton states in regularized dispersive equations”, Low Temp Phys, 34:7 (2008), 564  crossref  adsnasa  isi  scopus
    30. O. F. Oxtoby, I. V. Barashenkov, “Asymptotic expansion of the wobbling kink”, Theoret. and Math. Phys., 159:3 (2009), 863–869  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    31. Barashenkov I.V., Oxtoby O.F., “Wobbling Kinks in Phi(4) Theory”, Phys. Rev. E, 80:2, Part 2 (2009), 026608  crossref  adsnasa  isi  scopus
    32. Gani V.A., Ksenzov V.G., Kudryavtsev A.E., “Example of a Self-Consistent Solution for a Fermion on Domain Wall”, Phys. Atom. Nuclei, 73:11 (2010), 1889–1892  crossref  adsnasa  isi  elib  scopus
    33. Hertzberg M.P., “Quantum Radiation of Oscillons”, Phys. Rev. D, 82:4 (2010), 045022  crossref  adsnasa  isi  elib  scopus
    34. Romanczukiewicz T., Shnir Ya., “Oscillon Resonances and Creation of Kinks in Particle Collisions”, Phys. Rev. Lett., 105:8 (2010), 081601  crossref  adsnasa  isi  elib  scopus
    35. Baimova J.A., Bebikhov Yu.V., Dmitriev S.V., Khare A., Potekaev A.I., “Translationally Invariant Kink Solutions of Discrete Phi(4) Models”, Russ. Phys. J., 53:3 (2010), 231–238  crossref  zmath  isi  elib  scopus
    36. Smirnov L.I., “On the Wave Propagation of Concentration Hydrogen Disturbances in Palladium”, Phys. Metals Metallogr., 109:2 (2010), 107–110  crossref  adsnasa  isi  scopus
    37. Cuevas J., Koukouloyannis V., Kevrekidis P.G., Archilla J.F.R., “Multibreather and Vortex Breather Stability in Klein-Gordon Lattices: Equivalence Between Two Different Approaches”, Int. J. Bifurcation Chaos, 21:8 (2011), 2161–2177  crossref  zmath  isi  elib  scopus
    38. Demidov S.V., Levkov D.G., “Soliton Pair Creation in Classical Wave Scattering”, J. High Energy Phys., 2011, no. 6, 016  crossref  zmath  isi  elib  scopus
    39. Gani V.A., Ksenzov V.G., Kudryavtsev A.E., “Stable Branches of a Solution for a Fermion on Domain Wall”, Phys. Atom. Nuclei, 74:5 (2011), 771–777  crossref  adsnasa  isi  elib  scopus
    40. Halavanau A., Romanczukiewicz T., Shnir Ya., “Resonance Structures in Coupled Two-Component Phi(4) Model”, Phys. Rev. D, 86:8 (2012), 085027  crossref  adsnasa  isi  elib  scopus
    41. Ekomasov E.G., Murtazin R.R., Azamatov Sh.A., “Numerical Simulation of the Generation of Magnetic Inhomogeneities in Ferromagnets with Inhomogeneous Parameters”, Phys. Solid State, 54:8 (2012), 1584–1590  crossref  adsnasa  isi  elib  scopus
    42. Ekomasov E.G., Gumerov A.M., Murtazin R.R., “O vozbuzhdenii solitonov pri vzaimodeistvii kinkov uravneniya sinus-gordona s prityagivayuschei primesyu”, Kompyuternye issledovaniya i modelirovanie, 4:3 (2012), 509–520  elib
    43. Ya. M. Shnir, “Topological solitons”, Phys. Part. Nuclei Lett, 9:9-10 (2012), 745  crossref  adsnasa  elib  scopus
    44. Kryuchkov S.V., Kukhar' Egor I., “The Solitary Electromagnetic Waves in the Graphene Superlattice”, Physica B, 408 (2013), 188–192  crossref  adsnasa  isi  elib  scopus
    45. S.V. Kryuchkov, E.I. Kukhar’, D.V. Zav’yalov, “Charge dynamics in graphene and graphene superlattices under a high-frequency electric field: a semiclassical approach”, Laser Phys, 23:6 (2013), 065902  crossref  isi  elib  scopus
    46. Jesús Cuevas, P.G.. Kevrekidis, Avadh Saxena, Avinash Khare, “PT-symmetric dimer of coupled nonlinear oscillators”, Phys. Rev. A, 88:3 (2013)  crossref  isi  scopus
    47. S. P. Popov, “Influence of dislocations on kink solutions of the double sine-Gordon equation”, Comput. Math. Math. Phys., 53:12 (2013), 1891–1899  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    48. P. G. Kevrekidis, “Variational method for nonconservative field theories: Formulation and two <span class="aps-inline-formula"><math><mi mathvariant="script">PT</mi></math></span>-symmetric case examples”, Phys. Rev. A, 89:1 (2014)  crossref  isi  scopus
    49. A. M. Gumerov, E. G. Ekomasov, F. K. Zakir'yanov, R. V. Kudryavtsev, “Structure and properties of four-kink multisolitons of the sine-Gordon equation”, Comput. Math. Math. Phys., 54:3 (2014), 491–504  mathnet  crossref  crossref  isi  elib  elib
    50. V.A.. Gani, A.E.. Kudryavtsev, M.A.. Lizunova, “Kink interactions in the <span class="aps-inline-formula"><math xmlns="" display="inline"><mrow><mo stretchy="false">(</mo><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow><mo stretchy="false">)</mo></mrow></math></span>-dimensional <span class="aps-inline-formula"><math xmlns="" display="inline"><msup><mi>φ</mi><mn>6</mn></msup></math></span> model”, Phys. Rev. D, 89:12 (2014)  crossref  zmath  isi  scopus
    51. M. V. Charukhchyan, E. S. Sedov, S. M. Arakelian, A. P. Alodjants, “Spatially localized structures and oscillons in atomic Bose–Einstein condensates confined in optical lattices”, Phys. Rev. A, 89:6 (2014)  crossref  isi  scopus
    53. S. P. Popov, “Interactions of breathers and kink pairs of the double sine-Gordon equation”, Comput. Math. Math. Phys., 54:12 (2014), 1876–1885  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    54. Danial Saadatmand, S.V.. Dmitriev, D.I.. Borisov, P.G.. Kevrekidis, M.A.. Fatykhov, “Kink scattering from a parity-time-symmetric defect in the ϕ4 model”, Communications in Nonlinear Science and Numerical Simulation, 2015  crossref  isi  scopus
    55. JETP Letters, 101:7 (2015), 497–502  mathnet  crossref  crossref  isi  elib  elib
    56. E. G. Ekomasov, A. M. Gumerov, R. V. Kudryavtsev, “On the possibility of the observation of the resonance interaction between kinks of the sine-Gordon equation and localized waves in real physical systems”, JETP Letters, 101:12 (2015), 835–839  mathnet  crossref  crossref  isi  elib  elib
    57. Gani V.A., Lensky V., Lizunova M.A., “Kink Excitation Spectra in the (1+1)-Dimensional Phi(8) Model”, J. High Energy Phys., 2015, no. 8, 147  crossref  zmath  isi  scopus
    58. Derbov V.L. Grachev D.D. Sevastyanov L.A. Lovetskiy K.P. Vinitsky S.I. Gusev A.A., “Model For Spin Waves and Lasing in Monolayer Graphene Films”, Saratov Fall Meeting 2014: Optical Technologies in Biophysics and Medicine Xvi; Laser Physics and Photonics Xvi; and Computational Biophysics, Proceedings of Spie, 9448, ed. Genina E. Derbov V. Larin K. Postnov D. Tuchin V., Spie-Int Soc Optical Engineering, 2015, 94481W  crossref  isi  scopus
    59. Sedov E.S., Charukhchyan M.V., Arakelian S.M., Alodjants A.P., Chuang Y.-L., Lee R.-K., “Atomic Bose–Einstein Condensates as Nonlinear Hyperbolic Metamaterials”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 289–294  isi
    60. Simas F.C., Gomes A.R., Nobrega K.Z., Oliveira J. C. R. E., “Suppression of two-bounce windows in kink-antikink collisions”, J. High Energy Phys., 2016, no. 9, 104  crossref  isi  elib  scopus
    61. Gani V.A., Lensky V., Lizunova M.A., Mrozovskaya E.V., “Excitation spectra of solitary waves in scalar field models with polynomial self-interaction”, International Conference on Particle Physics and Astrophysics (Icppa-2015), Pts 1-4, Journal of Physics Conference Series, 675, IOP Publishing Ltd, 2016, 012019  crossref  isi  scopus
    62. Gani V.A., Lizunova M.A., Radomskiy R.V., “Scalar triplet on a domain wall”, International Conference on Particle Physics and Astrophysics (Icppa-2015), Pts 1-4, Journal of Physics Conference Series, 675, IOP Publishing Ltd, 2016, 012020  crossref  isi  scopus
    63. Marjaneha A.M., Saadatmand D., Zhouc K., Dmitriev S.V., Zomorrodiana M.E., “High energy density in the collision of N kinks in the 4 model”, Commun. Nonlinear Sci. Numer. Simul., 49 (2017), 30–38  crossref  mathscinet  isi  scopus
    64. Kudryavtsev A.E., Lizunova M.A., Phys. Rev. D, 95:5 (2017), 056009  crossref  mathscinet  isi  scopus
    65. Ekomasov E.G., Gumerov A.M., Kudryavtsev R.V., “Resonance dynamics of kinks in the sine-Gordon model with impurity, external force and damping”, J. Comput. Appl. Math., 312 (2017), 198–208  crossref  mathscinet  zmath  isi  scopus
    66. Marjaneh A.M., Gani V.A., Saadatmand D., Dmitriev S.V., Javidan K., “Multi-Kink Collisions in the Phi(6) Model”, J. High Energy Phys., 2017, no. 7, 028  crossref  isi  scopus
    67. Radomskiy R.V., Mrozovskaya E.V., Gani V.A., Christov I.C., “Topological Defects With Power-Law Tails”, International Conference on Particle Physics and Astrophysics, Journal of Physics Conference Series, 798, eds. Galper A., Petrukhin A., Taranenko A., Selyuzhenkov I., Skorokhvatov M., Rubin S., Dmitrenko V., Gur, IOP Publishing Ltd, 2017, UNSP 012087  crossref  isi  scopus
    68. F. Sh. Shokirov, “Dinamika vzaimodeistviya blokhovskikh domennykh granits v dvumernoi nelineinoi sigma-modeli”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:4 (2017), 132–144  mathnet  crossref  elib
    69. Demirkaya A., Decker R., Kevrekidis P.G., Christovc I.C., Saxena A., “Kink Dynamics in a Parametric Phi(6) System: a Model With Controllably Many Internal Modes”, J. High Energy Phys., 2017, no. 12, 071  crossref  isi  scopus
    70. S. P. Popov, “New compacton solutions of an extended Rosenau–Pikovsky equation”, Comput. Math. Math. Phys., 57:9 (2017), 1540–1549  mathnet  crossref  crossref  isi  elib  elib
    71. Saadatmand D., Borisov D.I., Kevrekidis P.G., Zhou K., Dmitriev S.V., “Resonant Interaction of Phi(4) Kink With Pt-Symmetric Perturbation With Spatially Periodic Gain/Loss Coefficient”, Commun. Nonlinear Sci. Numer. Simul., 56 (2018), 62–76  crossref  mathscinet  isi  scopus
    72. Marjaneh A.M., Askari A., Saadatmand D., Dmitriev S.V., “Extreme Values of Elastic Strain and Energy in sine-Gordon Multi-Kink Collisions”, Eur. Phys. J. B, 91:1 (2018)  crossref  isi  scopus
    73. Bazeia D., Belendryasova E., Gani V.A., “Scattering of Kinks of the Sinh-Deformed Phi(4) Model”, Eur. Phys. J. C, 78:4 (2018), 340  crossref  isi  scopus
    74. Gani V.A., Kirillov A.A., Rubin S.G., “Classical Transitions With the Topological Number Changing in the Early Universe”, J. Cosmol. Astropart. Phys., 2018, no. 4, 042  crossref  isi  scopus
    75. Gani V.A., Marjaneh A.M., Askari A., Belendryasova E., Saadatmand D., “Scattering of the Double sine-Gordon Kinks”, Eur. Phys. J. C, 78:4 (2018), 345  crossref  isi  scopus
    76. S. P. Popov, “Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion”, Comput. Math. Math. Phys., 58:3 (2018), 437–448  mathnet  crossref  crossref  isi  elib
    77. Ekomasov E.G., Gumerov A.M., Kudryavtsev R.V., Dmitriev S.V., Nazarov V.N., “Multisoliton Dynamics in the Sine-Gordon Model With Two Point Impurities”, Braz. J. Phys., 48:6 (2018), 576–584  crossref  isi  scopus
    78. Kevrekidis P.G., Danaila I., Caputo J.-G., Carretero-Gonzalez R., “Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability, and Dynamics”, Phys. Rev. E, 98:5 (2018), 052217  crossref  isi  scopus
    79. Belendryasova E., Gani V.A., “Scattering of the Phi(8) Kinks With Power-Law Asymptotics”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 414–426  crossref  isi  scopus
    80. Christov I.C., Decker R.J., Demirkaya A., Gani V.A., Kevrekidis P.G., Radomskiy V R., “Long-Range Interactions of Kinks”, Phys. Rev. D, 99:1 (2019), 016010  crossref  isi  scopus
  • Успехи физических наук Physics-Uspekhi
    Number of views:
    This page:312
    Full text:167
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019