Sakhnovich, L. A. 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 Cited in 5 Documents 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 Keywords:evolution of spectral data; nonlinear equations Citations:Zbl 0595.39003 PDFBibTeX XMLCite \textit{L. A. Sakhnovich}, Ukr. Math. J. 40, No. 4, 459--461 (1988; Zbl 0683.35068); translation from Ukr. Mat. Zh. 40, No. 4, 533--535 (1988) Full Text: DOI 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). 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.