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Two-dimensional Schrödinger operator: inverse scattering transform and evolutional equations. (English) Zbl 0609.35082
From the authors’ abstract: The inverse problem for the two-dimensional Schrödinger operator on the data from one energy level is solved in a special class of ”finite-zone” or ”algebraic” operators. This class seems to be dense among all smooth periodic Schrödinger operators. Evolutional equations associated with this problem are constructed.
Reviewer: T.Faulkner

MSC:
35R30Inverse problems for PDE
35J10Schrödinger operator
35Q99PDE of mathematical physics and other areas
35P25Scattering theory (PDE)
35A30Geometric theory for PDE, characteristics, transformations
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Full Text: DOI
References:
[1] Novikov, S. P.; Manakov, S. V.; Pitaevsky, L. P.; Zakharov, V. E.: Theory of soliton. The inverse scattering method. (1984)
[2] Manakov, S. V.: Uspehi mat. Nauk.. 31, 245 (1976)
[3] Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.: Sov. math. Dokl.. 17, 947-951 (1976)
[4] Krichever, I. M.: Uspehi mat. Nauk. 32, 198 (1977)
[5] Cherednik, I. V.: Dan sssr. 252, 1104 (1980)
[6] Veselov, A. P.; Novikov, S. P.: Dan sssr. 279, 20-24 (1984)
[7] Veselov, A. P.; Novikov, S. P.: Dan sssr. 279, 784-788 (1984)
[8] Dubrovin, V. A.: Uspehi mat. Nauk. 36, 11 (1981)
[9] Krichever, I. M.; Novikov, S. P.: Uspehi mat. Nauk. 35, 47 (1980)
[10] Novikov, S. P.: Sov. math. Dokl.. 23 (1981)
[11] Krichever, I. M.: Dan sssr. 282 (1985)
[12] Grinevitch, P. G.; Novikov, R. G.: Funkt. analys i ego prilog.. 4 (1985)