Bright and dark soliton solutions for the complex Kundu-Eckhaus equation

Abstract

The main target of this article is to realize bright and dark soliton solutions to the complex Kundu-Eckhaus equation which represents a general form of integrable system that is gauge-equivalent to the mixed nonlinear Schrödinger equation. This soliton solution which represents the propagation of the ultra-short femtosecond pulses and the rogue wave in an optical fiber achieved for the first time in the framework of the solitary wave ansatz method. Furthermore, in this connection at the same time and parallel the extended simple equation method has been successfully applied to achieve new impressive solitary wave solutions to this model. A comparison between the obtained results and that satisfied in previous work is established.