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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

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
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