An exact solution for a derivative nonlinear Schrödinger equation

Abstract

A method of solution for the ’’derivative nonlinear Schrödinger equation’’ iq_t=−q_xx±i (q*q²)_x is presented. The appropriate inverse scattering problem is solved, and the one‐soliton solution is obtained, as well as the infinity of conservation laws. Also, we note that this equation can also possess ’’algebraic solitons.’’