zbMATH — the first resource for mathematics

On the two-dimensional Zakharov-Shabat problem. (English. Russian original) Zbl 0639.35067
Theor. Math. Phys. 72, No. 1, 790-793 (1987); translation from Teor. Mat. Fiz. 72, No. 1, 155-159 (1987).
An inverse scattering problem that is a natural two-dimensional analog of the Zakharov-Shabat problem is solved. The equations that can be integrated by means of this problem are considered.
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
Full Text: DOI
[1] V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, The Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980). · Zbl 0598.35002
[2] L. V. Bogdanov, Teor. Mat. Fiz.,70, 309 (1987).
[3] M. J. Ablovitz, D. Bar Yaacov, and A. S. Focas, Studies Appl. Math.,69, 135 (1983).
[4] S. V. Manakov, Physics D,3, 420 (1981). · Zbl 1194.35507
[5] V. E. Zakharov and S. V. Manakov, Funktsional. Analiz i Ego Prilozhen.,19, 11 (1985).
[6] P. G. Grinevich and S. V. Manakov, Funktsional. Analiz i Ego Prilozhen.,20, 14 (1986).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.