Soliton solutions of generalized Kundu-Eckhaus equation with an extra-dispersion via improved modified extended tanh-function technique

Abstract

In this paper, we introduce the generalized Kundu-Eckhaus equation (KEE) with extra-dispersion, which describes the propagation of the ultra-short femtosecond pulses in an optical fiber. Many exact solutions are constructed with the aid of improved modified extended tanh-function method and a new transformation. As a result, we have found a variety of new families of exact traveling wave solutions including bright solitons, dark solitons, singular solitons, Weierstrass elliptic doubly periodic solutions, Jacobi elliptic solutions, periodic solutions and rational solutions. Physical interpretation for some of the obtained solutions are illustrated in Figures.