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Zap. Nauchn. Sem. LOMI, 1984, Volume 133, Pages 77–91 (Mi znsl4411)  

This article is cited in 9 scientific papers (total in 9 papers)

Multidimensional integrable nonlinear systems and methods for constructing their solutions

V. E. Zakharov, S. V. Manakov


Abstract: A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of the nonlocal Riemann problem in presented. The method generalizes the local Riemann problem approach to the case of several space variables and incorporates the well-known Zakharov–Shabat dressing method.

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Bibliographic databases:

Document Type: Article
UDC: 519.4

Citation: V. E. Zakharov, S. V. Manakov, “Multidimensional integrable nonlinear systems and methods for constructing their solutions”, Differential geometry, Lie groups and mechanics. Part VI, Zap. Nauchn. Sem. LOMI, 133, "Nauka", Leningrad. Otdel., Leningrad, 1984, 77–91

Citation in format AMSBIB
\Bibitem{ZakMan84}
\by V.~E.~Zakharov, S.~V.~Manakov
\paper Multidimensional integrable nonlinear systems and methods for constructing their solutions
\inbook Differential geometry, Lie groups and mechanics. Part~VI
\serial Zap. Nauchn. Sem. LOMI
\yr 1984
\vol 133
\pages 77--91
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4411}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=742150}
\zmath{https://zbmath.org/?q=an:0553.35078}


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  • http://mi.mathnet.ru/eng/znsl/v133/p77

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    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. 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
    2. P. G. Grinevich, R. G. Novikov, “Analogs of multisoliton potentials for the two-dimensional Schrödinger operator”, Funct. Anal. Appl., 19:4 (1985), 276–285  mathnet  crossref  mathscinet  zmath  isi
    3. R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. I. Inverse scattering method”, Theoret. and Math. Phys., 75:3 (1988), 555–566  mathnet  crossref  mathscinet  isi
    5. B. I. Suleimanov, I. T. Habibullin, “Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes”, Theoret. and Math. Phys., 97:2 (1993), 1250–1258  mathnet  crossref  mathscinet  zmath  isi
    6. Theoret. and Math. Phys., 99:2 (1994), 505–510  mathnet  crossref  mathscinet  zmath  isi
    7. 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
    8. 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
    9. Sergeev S.M., “Quantization of Three-Wave Equations”, J. Phys. A-Math. Theor., 40:42 (2007), 12709–12724  crossref  zmath  isi  elib
  • Записки научных семинаров ПОМИ
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