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Evolution of spectral data and nonlinear equations. (English. Russian original) Zbl 0683.35068

Ukr. Math. J. 40, No. 4, 459-461 (1988); translation from Ukr. Mat. Zh. 40, No. 4, 533-535 (1988).
Yu. M. Berezanskij [Sov. Math., Dokl. 31, 264-267 (1985); translation from Dokl. Akad. Nauk SSSR 281, 16-19 (1985; Zbl 0595.39003)], considered the equation \(G_ t-F_ x+[G,F]=0\) where [G,F] is a commutator. Evolution of spectral data is used to semi-infinite discrete problems. In this paper an evolution law is explained for spectral data in a continuous case. This admits to study a mixed problem in the region \(0\leq x<\infty\), \(t\geq 0\).
Reviewer: J.H.Tian

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35R30 Inverse problems for PDEs
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations

Citations:

Zbl 0595.39003
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References:

[1] S. P. Novikov (ed.), Theory of Solitons, Method of the Inverse Problem [in Russian], Nauka, Moscow (1980).
[2] Yu. M. Berezanskii, ?Integration of nonlinear difference equations by the method of the inverse problem,? Dokl. Akad. Nauk SSSR,281, No. 1, 16-19 (1985).
[3] L. A. Sakhnovich, ?Problems of factorization and operator identities,? Usp. Mat. Nauk,41, No. 1, 3-55 (1986).
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