General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Funktsional. Anal. i Prilozhen.:

Personal entry:
Save password
Forgotten password?

Funktsional. Anal. i Prilozhen., 1974, Volume 8, Issue 3, Pages 43–53 (Mi faa2357)  

This article is cited in 118 scientific papers (total in 118 papers)

A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I

V. E. Zakharov, A. B. Shabat

Full text: PDF file (985 kB)

English version:
Functional Analysis and Its Applications, 1974, 8:3, 226–235

Bibliographic databases:

Received: 14.03.1974

Citation: V. E. Zakharov, A. B. Shabat, “A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I”, Funktsional. Anal. i Prilozhen., 8:3 (1974), 43–53; Funct. Anal. Appl., 8:3 (1974), 226–235

Citation in format AMSBIB
\by V.~E.~Zakharov, A.~B.~Shabat
\paper A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
\jour Funktsional. Anal. i Prilozhen.
\yr 1974
\vol 8
\issue 3
\pages 43--53
\jour Funct. Anal. Appl.
\yr 1974
\vol 8
\issue 3
\pages 226--235

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Non-linear equations of Korteweg–de Vries type, finite-zone linear operators, and Abelian varieties”, Russian Math. Surveys, 31:1 (1976), 59–146  mathnet  crossref  mathscinet  zmath
    2. B. A. Dubrovin, “Konechnozonnye lineinye differentsialnye operatory i abelevy mnogoobraziya”, UMN, 31:4(190) (1976), 259–260  mathnet  mathscinet  zmath
    3. P. P. Kulish, “Factorization of the classical and the quantum $S$-matrix and conservation laws”, Theoret. and Math. Phys., 26:2 (1976), 132–137  mathnet  crossref  mathscinet
    4. V. E. Zakharov, S. V. Manakov, “Generalization of the inverse scattering problem method”, Theoret. and Math. Phys., 27:3 (1976), 485–487  mathnet  crossref  mathscinet  zmath
    5. S. V. Manakov, “Metod obratnoi zadachi rasseyaniya i dvumernye evolyutsionnye uravneniya”, UMN, 31:5(191) (1976), 245–246  mathnet  mathscinet  zmath
    6. I. M. Krichever, “Algebraic curves and commuting matricial differential operators”, Funct. Anal. Appl., 10:2 (1976), 144–146  mathnet  crossref  mathscinet  zmath
    7. I. M. Krichever, “Methods of algebraic geometry in the theory of non-linear equations”, Russian Math. Surveys, 32:6 (1977), 185–213  mathnet  crossref  mathscinet  zmath
    8. I. M. Krichever, “Integration of nonlinear equations by the methods of algebraic geometry”, Funct. Anal. Appl., 11:1 (1977), 12–26  mathnet  crossref  mathscinet  zmath
    9. B. A. Dubrovin, “Completely integrable Hamiltonian systems associated with matrix operators and Abelian varieties”, Funct. Anal. Appl., 11:4 (1977), 265–277  mathnet  crossref  mathscinet  zmath
    10. V. A. Andreev, “On the connection between “pseudopotentials” and the inverse scattering problem method”, Theoret. and Math. Phys., 36:3 (1978), 773–779  mathnet  crossref  mathscinet  zmath
    11. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286  mathnet  crossref  mathscinet  zmath
    12. L. A. Takhtadzhyan, L. D. Faddeev, “The quantum method of the inverse problem and the Heisenberg $XYZ$ model”, Russian Math. Surveys, 34:5 (1979), 11–68  mathnet  crossref  mathscinet
    13. E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantum inverse problem method. I”, Theoret. and Math. Phys., 40:2 (1979), 688–706  mathnet  crossref  mathscinet  isi
    14. V. E. Zakharov, A. B. Shabat, “Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II”, Funct. Anal. Appl., 13:3 (1979), 166–174  mathnet  crossref  mathscinet  zmath
    15. L. A. Sakhnovich, “Factorization of operators in $L^2(a,b)$”, Funct. Anal. Appl., 13:3 (1979), 187–192  mathnet  crossref  mathscinet  zmath
    16. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over algebraic curves and non-linear equations”, Russian Math. Surveys, 35:6 (1980), 53–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. I. M. Krichever, “Elliptic solutions of the Kadomtsev–Petviashvili equation and integrable systems of particles”, Funct. Anal. Appl., 14:4 (1980), 282–290  mathnet  crossref  mathscinet  zmath  isi
    18. V. P. Maslov, G. A. Omel'yanov, “Asymptotic soliton-form solutions of equations with small dispersion”, Russian Math. Surveys, 36:3 (1981), 73–149  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47  mathnet  crossref  mathscinet  zmath  isi
    20. S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. B. M. Levitan, “Approximation of infinite-zone potentials by finite-zone potentials”, Math. USSR-Izv., 20:1 (1983), 55–87  mathnet  crossref  mathscinet  zmath
    22. L. P. Nizhnik, M. D. Pochinaiko, “Integration of the nonlinear two-dimensional spatial Schrodinger equation by the inverse-problem method”, Funct. Anal. Appl., 16:1 (1982), 66–69  mathnet  crossref  mathscinet  zmath  isi
    23. A. N. Leznov, “The inverse scattering method in a form invariant with respect to representations of the internal symmetry algebra”, Theoret. and Math. Phys., 58:1 (1984), 103–106  mathnet  crossref  mathscinet  isi
    24. I. M. Krichever, “The laplace method, algebraic curves, and nonlinear equations”, Funct. Anal. Appl., 18:3 (1984), 210–223  mathnet  crossref  mathscinet  zmath  isi
    25. A. N. Leznov, V. I. Man'ko, S. M. Chumakov, “Symmetries and soliton solutions of nonlinear equations”, Theoret. and Math. Phys., 63:1 (1985), 356–365  mathnet  crossref  mathscinet  zmath  isi
    26. V. E. Zakharov, S. V. Manakov, “Construction of higher-dimensional nonlinear integrable systems and of their solutions”, Funct. Anal. Appl., 19:2 (1985), 89–101  mathnet  crossref  mathscinet  zmath  isi
    27. I. M. Krichever, “Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model”, Funct. Anal. Appl., 20:3 (1986), 203–214  mathnet  crossref  mathscinet  zmath  isi
    28. V. D. Lipovskii, “Hamiltonian structure of the Kadomtsev–Petviashvili–II equation in the class of decreasing Cauchy data”, Funct. Anal. Appl., 20:4 (1986), 282–291  mathnet  crossref  mathscinet  zmath  isi
    29. R. A. Sharipov, “Multiplet solutions of the Kadomtsev–Petviashvili equation against a finite-zone background”, Russian Math. Surveys, 42:5 (1987), 177–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    30. L. V. Bogdanov, “Veselov–Novikov equation as a natural two-dimensional generalization of the Korteweg–de Vries equation”, Theoret. and Math. Phys., 70:2 (1987), 219–223  mathnet  crossref  mathscinet  zmath  isi
    31. B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, Math. USSR-Izv., 32:2 (1989), 269–288  mathnet  crossref  mathscinet  zmath
    32. I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213  mathnet  crossref  mathscinet  zmath  isi
    33. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    34. T. V. Red'kina, “Some properties of the complexification of the KdV equation”, Math. USSR-Izv., 39:3 (1992), 1251–1261  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    35. T. M. Malanyuk, “A class of exact solutions of the Kadomtsev–Petviashvili equation”, Russian Math. Surveys, 46:3 (1991), 225–227  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    36. V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Generation of new exactly solvable potentials of a nonstationary Schrödinger equation”, Theoret. and Math. Phys., 87:3 (1991), 635–640  mathnet  crossref  mathscinet  zmath  isi
    37. I. A. Anders, V. P. Kotlyarov, E. Ya. Khruslov, “Curved asymptotic solitons of the Kadomtsev–Petviashvili equation”, Theoret. and Math. Phys., 99:1 (1994), 402–408  mathnet  crossref  mathscinet  zmath  isi
    38. A. I. Zenchuk, S. V. Manakov, “The dual $\overline \partial$-problem, $(2+1)$-dimensional nonlinear evolution equations and their reductions”, Theoret. and Math. Phys., 105:3 (1995), 1490–1499  mathnet  crossref  mathscinet  zmath  isi
    39. R. R. Gadyl'shin, O. M. Kiselev, “On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II”, Theoret. and Math. Phys., 106:2 (1996), 167–173  mathnet  crossref  crossref  mathscinet  zmath  isi
    40. D. Yu. Ostapenko, A. P. Pal-Val, E. Ya. Khruslov, “Uniform asymptotic formulas for the curved solitons of the Kadomtsev–Petviashvili equations”, Theoret. and Math. Phys., 108:2 (1996), 1013–1018  mathnet  crossref  crossref  mathscinet  zmath  isi
    41. D. V. Yur'ev, “Topics in isotopic pairs and their representations. II. A general supercase”, Theoret. and Math. Phys., 111:1 (1997), 511–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    42. P. Winternitz, A. Yu. Orlov, “$P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators”, Theoret. and Math. Phys., 113:2 (1997), 1393–1417  mathnet  crossref  crossref  mathscinet  isi
    43. O. M. Kiselev, “An asymptotic solution of the Cauchy problem for the Davey–Stewartson-I equation”, Theoret. and Math. Phys., 114:1 (1998), 81–89  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    44. O. M. Kiselev, “Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients”, Sb. Math., 190:2 (1999), 233–254  mathnet  crossref  crossref  mathscinet  zmath  isi
    45. A. I. Zenchuk, “Miura-type transformations of nonlinear partial differential equations integrable by the $\bar\partial$-problem method”, Theoret. and Math. Phys., 119:1 (1999), 431–437  mathnet  crossref  crossref  mathscinet  zmath  isi
    46. A. B. Shabat, “Third version of the dressing method”, Theoret. and Math. Phys., 121:1 (1999), 1397–1408  mathnet  crossref  crossref  mathscinet  zmath  isi
    47. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Bäcklund and Darboux Transformations for the Nonstationary Schrödinger Equation”, Proc. Steklov Inst. Math., 226 (1999), 42–62  mathnet  mathscinet  zmath
    48. Krichever, I, “Periodic and almost-periodic potentials in inverse problems”, Inverse Problems, 15:6 (1999), R117  isi
    49. P. G. Grinevich, “Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity”, Russian Math. Surveys, 55:6 (2000), 1015–1083  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    50. S. B. Leble, “Covariance of Lax Pairs and Integrability of the Compatibility Condition”, Theoret. and Math. Phys., 128:1 (2001), 890–905  mathnet  crossref  crossref  mathscinet  zmath  isi
    51. A. Yu. Orlov, D. M. Shcherbin, “Hypergeometric Solutions of Soliton Equations”, Theoret. and Math. Phys., 128:1 (2001), 906–926  mathnet  crossref  crossref  mathscinet  zmath  isi
    52. G. A. Alekseev, “A New Integral Equation Form of Integrable Reductions of the Einstein Equations”, Theoret. and Math. Phys., 129:2 (2001), 1466–1483  mathnet  crossref  crossref  mathscinet  zmath  isi
    53. A. Yu. Orlov, “Hypergeometric Functions Related to Schur $Q$-Polynomials and the $B$KP Equation”, Theoret. and Math. Phys., 137:2 (2003), 1574–1589  mathnet  crossref  crossref  mathscinet  zmath  isi
    54. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    55. JETP Letters, 77:6 (2003), 324–327  mathnet  crossref
    56. E. V. Gudkova, I. T. Habibullin, “Kadomtsev–Petviashvili Equation on the Half-Plane”, Theoret. and Math. Phys., 140:2 (2004), 1086–1094  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    57. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    58. I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funct. Anal. Appl., 38:2 (2004), 138–148  mathnet  crossref  crossref  mathscinet  zmath  isi
    59. De Monvel A.B. Fokas A.S. Shepelsky D., “The Mkdv Equation on the Half-Line”, J. Inst. Math. Jussieu, 3:2 (2004), 139–164  crossref  isi
    60. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrödinger Equation with a Bidimensionally Perturbed One-Dimensional Potential”, Proc. Steklov Inst. Math., 251 (2005), 6–48  mathnet  mathscinet  zmath
    61. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential”, Theoret. and Math. Phys., 144:2 (2005), 1100–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    62. de Monvel, AB, “Characteristic properties of the scattering data for the mKdV equation on the half-line”, Communications in Mathematical Physics, 253:1 (2005), 51  crossref  isi
    63. A. Yu. Orlov, “Hypergeometric Functions as Infinite-Soliton Tau Functions”, Theoret. and Math. Phys., 146:2 (2006), 183–206  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    64. P. B. Djakov, B. S. Mityagin, “Instability zones of periodic 1-dimensional Schrödinger and Dirac operators”, Russian Math. Surveys, 61:4 (2006), 663–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    65. JETP Letters, 83:10 (2006), 462–466  mathnet  crossref  isi
    66. A. K. Pogrebkov, “Commutator identities on associative algebras and the integrability of nonlinear evolution equations”, Theoret. and Math. Phys., 154:3 (2008), 405–417  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    67. Vladimir S. Gerdjikov, Nikolay A. Kostov, “Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type”, SIGMA, 4 (2008), 029, 30 pp.  mathnet  crossref  mathscinet  zmath
    68. J. Harnad, A. Yu. Orlov, “Fermionic approach for evaluating integrals of rational symmetric functions”, Theoret. and Math. Phys., 158:1 (2009), 17–39  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    69. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Building an extended resolvent of the heat operator via twisting transformations”, Theoret. and Math. Phys., 159:3 (2009), 721–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    70. K. R. Khusnutdinova, A. M. Samsonov, A. S. Zakharov, “Nonlinear long-wave models for imperfectly bonded layered waveguides”, Theoret. and Math. Phys., 159:3 (2009), 819–832  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    71. V. G. Dubrovskii, A. V. Gramolin, “Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations”, Theoret. and Math. Phys., 160:1 (2009), 905–916  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    72. V. S. Gerdjikov, G. G. Grahovski, “Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory”, SIGMA, 6 (2010), 044, 29 pp.  mathnet  crossref  mathscinet
    73. Aristophanes Dimakis, Folkert Müller-Hoissen, “Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions”, SIGMA, 6 (2010), 055, 27 pp.  mathnet  crossref  mathscinet
    74. St. Petersburg Math. J., 22:3 (2011), 473–483  mathnet  crossref  mathscinet  zmath  isi
    75. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, Theoret. and Math. Phys., 165:1 (2010), 1237–1255  mathnet  crossref  crossref  adsnasa  isi
    76. V. G. Dubrovskii, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions with functional parameters of the Nizhnik–Veselov–Novikov equation with constant asymptotic values at infinity”, Theoret. and Math. Phys., 165:2 (2010), 1470–1489  mathnet  crossref  crossref  isi
    77. Atkinson J., Nijhoff F., “A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations”, Comm Math Phys, 299:2 (2010), 283–304  crossref  isi
    78. Dimakis A., Mueller-Hoissen F., “KP line solitons and Tamari lattices”, Journal of Physics A-Mathematical and Theoretical, 44:2 (2011), 025203  crossref  isi
    79. V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method”, Theoret. and Math. Phys., 167:3 (2011), 725–739  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    80. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Properties of the solitonic potentials of the heat operator”, Theoret. and Math. Phys., 168:1 (2011), 865–874  mathnet  crossref  crossref  mathscinet  isi
    81. Andrei V. Zotov, “$1+1$ Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp.  mathnet  crossref  mathscinet
    82. Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov, Tihomir I. Valchev, “Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces”, SIGMA, 7 (2011), 096, 48 pp.  mathnet  crossref  mathscinet
    83. Treibich A., “Nonlinear evolution equations and hyperelliptic covers of elliptic curves”, Regular & Chaotic Dynamics, 16:3–4 (2011), 290–310  crossref  isi
    84. Badanin A., Korotyaev E.L., “Even Order Periodic Operators on the Real Line”, Int Math Res Not, 2012, no. 5, 1143–1194  isi
    85. V. L. Vereshchagin, “Integrable boundary conditions for $(2+1)$-dimensional models of mathematical physics”, Theoret. and Math. Phys., 171:3 (2012), 792–799  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    86. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Extended resolvent of the heat operator with a multisoliton potential”, Theoret. and Math. Phys., 172:2 (2012), 1037–1051  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    87. V. L. Vereshchagin, “Explicit Solutions of Boundary-Value Problems for $(2+1)$-Dimensional Integrable Systems”, Math. Notes, 93:3 (2013), 360–372  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    88. A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    89. I. T. Habibullin, M. V. Yangubaeva, “Formal diagonalization of a discrete Lax operator and conservation laws and symmetries of dynamical systems”, Theoret. and Math. Phys., 177:3 (2013), 1655–1679  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    90. A. I. Zenchuk, “Solutions of multidimensional partial differential equations representable as a one-dimensional flow”, Theoret. and Math. Phys., 178:3 (2014), 299–313  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    91. E. Sh. Gutshabash, “Nonlinear sigma model, Zakharov–Shabat method, and new exact forms of the minimal surfaces in ${\mathbb R}^3$”, JETP Letters, 99:12 (2014), 715–719  mathnet  crossref  crossref  isi  elib  elib
    92. Bernd Fritzsche, Bernd Kirstein, Inna Ya. Roitberg, Alexander L. Sakhnovich, “Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables”, SIGMA, 11 (2015), 010, 13 pp.  mathnet  crossref  mathscinet
    93. V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, “The $N$-wave equations with $\mathcal{PT}$ symmetry”, Theoret. and Math. Phys., 188:3 (2016), 1305–1321  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    94. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
    95. A. I. Zenchuk, “Multidimensional linearizable system of $n$-wave-type equations”, Theoret. and Math. Phys., 190:1 (2017), 43–51  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    96. JETP Letters, 105:2 (2017), 125–129  mathnet  crossref  crossref  isi  elib
    97. I. T. Habibullin, A. R. Khakimova, “Invariant manifolds and Lax pairs for integrable nonlinear chains”, Theoret. and Math. Phys., 191:3 (2017), 793–810  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    98. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    99. V. S. Gerdjikov, “Kulish–Sklyanin-type models: Integrability and reductions”, Theoret. and Math. Phys., 192:2 (2017), 1097–1114  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    100. A. Yu. Orlov, “Hurwitz numbers and products of random matrices”, Theoret. and Math. Phys., 192:3 (2017), 1282–1323  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    101. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    102. Natanzon S.M. Orlov A.Yu., “BKP and Projective Hurwitz Numbers”, Lett. Math. Phys., 107:6 (2017), 1065–1109  crossref  isi
    103. Carlet G. Casati M. Shadrin S., “Normal Forms of Dispersive Scalar Poisson Brackets With Two Independent Variables”, Lett. Math. Phys., 108:10 (2018), 2229–2253  crossref  isi
    104. Zhang N. Xia T.-ch. Fan E.-g., “A Riemann–Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line”, Acta Math. Appl. Sin.-Engl. Ser., 34:3 (2018), 493–515  crossref  isi
    105. Jen-Hsu Chang, “Asymptotic analysis of multilump solutions of the Kadomtsev–Petviashvili-I equation”, Theoret. and Math. Phys., 195:2 (2018), 676–689  mathnet  crossref  crossref  adsnasa  isi  elib
    106. I. T. Habibullin, A. R. Khakimova, “A direct algorithm for constructing recursion operators and Lax pairs for integrable models”, Theoret. and Math. Phys., 196:2 (2018), 1200–1216  mathnet  crossref  crossref  adsnasa  isi  elib
    107. G. G. Grahovski, A. Mohammed, H. Susanto, “Nonlocal reductions of the Ablowitz–Ladik equation”, Theoret. and Math. Phys., 197:1 (2018), 1412–1429  mathnet  crossref  crossref  adsnasa  isi  elib
    108. G. G. Grahovski, A. J. Mustafa, H. Susanto, “Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces”, Theoret. and Math. Phys., 197:1 (2018), 1430–1450  mathnet  crossref  crossref  adsnasa  isi  elib
    109. P. G. Grinevich, P. M. Santini, “Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case”, Theoret. and Math. Phys., 196:3 (2018), 1294–1306  mathnet  crossref  crossref  adsnasa  isi  elib
    110. A. R. Khakimova, “On description of generalized invariant manifolds for nonlinear equations”, Ufa Math. J., 10:3 (2018), 106–116  mathnet  crossref  isi
    111. A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, Theoret. and Math. Phys., 197:3 (2018), 1779–1796  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    112. Simonetta Abenda, Petr G. Grinevich, “Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case”, Proc. Steklov Inst. Math., 302 (2018), 1–15  mathnet  crossref  crossref  isi  elib
    113. Music M. Perry P., “Global Solutions For the Zero-Energy Novikov-Veselov Equation By Inverse Scattering”, Nonlinearity, 31:7 (2018), 3413–3440  crossref  mathscinet  zmath  isi  scopus
    114. P. G. Grinevich, P. M. Santini, “The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes”, Russian Math. Surveys, 74:2 (2019), 211–263  mathnet  crossref  crossref  adsnasa  isi  elib
    115. H. Wajahat W. A. Riaz, M. Hassan, “Dressing method for the multicomponent short-pulse equation”, Theoret. and Math. Phys., 199:2 (2019), 709–718  mathnet  crossref  crossref  adsnasa  isi  elib
    116. I. T. Khabibullin, A. R. Khakimova, “Invariantnye mnogoobraziya integriruemykh uravnenii giperbolicheskogo tipa i ikh prilozheniya”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 136–150  mathnet  mathscinet
    117. A. V. Zabrodin, “Matrix modified Kadomtsev–Petviashvili hierarchy”, Theoret. and Math. Phys., 199:3 (2019), 771–783  mathnet  crossref  crossref  adsnasa  isi  elib
    118. V. S. Gerdjikov, A. A. Stefanov, I. D. Iliev, G. P. Boyadjiev, A. O. Smirnov, V. B. Matveev, M. V. Pavlov, “Recursion operators and hierarchies of $mKdV$ equations related to the Kac–Moody algebras $D_4^{(1)}$, $D_4^{(2)}$, and $D_4^{(3)}$”, Theoret. and Math. Phys., 204:3 (2020), 1110–1129  mathnet  crossref  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:2392
    Full text:1002
    First page:2

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020