On the complex modified Korteweg–de Vries equation with a self-consistent source and nonzero boundary conditions

Abstract

UDC 517.957

We study the method of inverse scattering transform for defocusing complex modified Korteweg–de-Vries (cmKdV) equation with self-consistent sources (SCS) and nonzero boundary conditions at infinity. We prove a theorem on the evolution of the scattering data for a self-adjoint Zakharov–Shabat system in which the potential is a solution of the defocusing cmKdV equation with SCS. The obtained results enable us to solve the inverse scattering problem for the self-adjoint Zakharov–Shabat system with a potential from the class of functions nonvanishing at infinity.