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This article is cited in 516 scientific papers (total in 516 papers)
Non-linear equations of Korteweg–de Vries type, finite-zone linear
operators, and Abelian varieties
B. A. Dubrovin, V. B. Matveev, S. P. Novikov
Abstract:
The basic content of this survey is an exposition of a recently developed method of constructing a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable. These solutions are such that the spectrum of their associated linear differential operators has a finite-zone structure. The set of linear operators with a given finite-zone spectrum is the Jacobian variety of a Riemann surface, which is determined by the structure of the spectrum. We give an explicit solution of the corresponding non-linear equations in the language of the theory of Abelian functions.
Received: 02.06.1975
Citation:
B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Non-linear equations of Korteweg–de Vries type, finite-zone linear
operators, and Abelian varieties”, Uspekhi Mat. Nauk, 31:1(187) (1976), 55–136; Russian Math. Surveys, 31:1 (1976), 59–146
Linking options:
https://www.mathnet.ru/eng/rm3642https://doi.org/10.1070/RM1976v031n01ABEH001446 https://www.mathnet.ru/eng/rm/v31/i1/p55
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Abstract page: | 3489 | Russian version PDF: | 1850 | English version PDF: | 55 | References: | 145 | First page: | 8 |
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