Inverse scattering transform for general matrix Schrodinger operators and the related symplectic structure

The general matrix Schrodinger problem is studied and the corresponding equations for the inverse scattering method are obtained. Appropriate modifications lead to a derivation of the generalised Gel'fand-Levitan-Marchenko equations for the case in which there are double poles of the matrix A-1(k). The symplectic structure associated with the non-linear evolution equations of this formalism is also investigated. Special attention is paid to the derivation of the Poisson bracket of the reflection coefficients.

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