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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.
MSC:
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
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[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).
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