Expansions over the 'squared' solutions and the inhomogeneous nonlinear Schrodinger equation

Abstract

The inhomogeneous nonlinear Schrodinger equation (INLSE) with vanishing boundary conditions is studied using the expansions over the 'squared' solutions of the Zakharov-Shabat system L. The authors stress the importance of the expansions over the so-called symplectic basis, which lead to a system of evolution equations for the scattering data that is easily solved for a generic choice of the inhomogeneity G(x,t). Sufficient (although unexplicit) conditions on G(x,t) are given, which ensure the integrability of the corresponding INLSE. It is known that each INLSE allows a Lax representation, the Lax operator being provided by L. In this respect they report that the corresponding M operator for G not=0 possesses pole singularities located on the spectrum of L. The INLSE occurs in plasma wave interactions.