Nonlinear integrable systems via general local matrix -problem

Abstract

Based on the matrix Riemann spectral problem a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolutions is proposed. Having introduced a normalization matrix to exclude the discrete spectrum from consideration, one follows the -problem scheme proposed by Leon to obtain the Lax pair. In this approach the spectral transform matrix R is responsible only for the continuous spectrum, while the evolution of the discrete spectrum is obtained as a consequence of the evolution of the continuous one.