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

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:
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
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
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
4. V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. I. Inverse scattering method”, Theoret. and Math. Phys., 75:3 (1988), 555–566
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
6. Theoret. and Math. Phys., 99:2 (1994), 505–510
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
8. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
9. Sergeev S.M., “Quantization of Three-Wave Equations”, J. Phys. A-Math. Theor., 40:42 (2007), 12709–12724