Generalized Matrix Form of the Inverse Scattering Method

Abstract

This is a review on the matrix generalization of the inverse scattering method. First, the inverse scattering problem for n × n Schrodinger equation is discussed. Second, the inverse scattering method is extended into n × n matrix form. Nonlinear evolution equations which are solvable by the extension are presented. In addition, it is pointed out that the same generalization is possible for discrete cases (lattice problems).