Some new nonlinear evolution equations integrable by the inverse problem method. (English. Russian original) Zbl 0558.35063

Mel’nikov, V. K.

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

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