On traveling wave solutions of the Kundu–Eckhaus equation

Abstract

The Kundu–Eckhaus equation is considered taking into account the traveling wave reduction. Nonlinear ordinary differential equation is shown to pass the weak Painlev e test in case when the Cauchy problem for the Kundu–Eckhaus equation is solved by the inverse scattering transform. However the general solution of nonlinear ordinary differential equation exist for more general case. This solution is given in this paper.