Soliton, Positon and Negaton Solutions to a Schrödinger Self-consistent Source Equation

Abstract

A Darboux transformation is furnished for a Schrödinger self-consistent source equation, along with a solution formula. Soliton, positon and negaton solutions to the Schrödinger self-consistent source equation are further constructed. The resulting solutions resemble those of the KdV equation with self-consistent sources, but the space and time variables are involved in a slightly different manner.