Mel’nikov, V. K. Some new nonlinear evolution equations integrable by the inverse problem method. (English. Russian original) Zbl 0558.35063 Math. USSR, Sb. 49, 461-489 (1984); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 469-498 (1983). The inverse scattering method is used to study the nonlinear evolution equations corresponding to the matrix relation \(\partial {\mathcal L}/\partial t+[{\mathcal A},{\mathcal L}-\eta I]={\mathcal B}({\mathcal L}-\eta I).\) Here \({\mathcal A}\) and \({\mathcal B}\) are differential operators, \(I=diag(1,0,...,0),\) \({\mathcal L}\) is also a differential operator with a special matrix structure. Reviewer: D.Yafaev Cited in 5 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35P25 Scattering theory for PDEs 35R30 Inverse problems for PDEs Keywords:inverse scattering method; nonlinear evolution equations PDF BibTeX XML Cite \textit{V. K. Mel'nikov}, Math. USSR, Sb. 49, 461--489 (1984; Zbl 0558.35063); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 469--498 (1983) Full Text: DOI