Optical soliton and bright–dark solitary wave solutions of nonlinear complex Kundu–Eckhaus dynamical equation of the ultra-short femtosecond pulses in an optical fiber

Abstract

In this research, we examine exact and solitary traveling solutions of nonlinear complex Kundu–Eckhaus equation with variable coefficients. Nonlinear complex Kundu–Eckhaus equation model has vital role in description of the proliferation of the pulses of the ultra-short femto second in an optical fiber, weakly nonlinear fragmented water waves, nonlinear optics and the quantum field theory. We implement a new auxiliary equation method and novel \(\left( \frac{G^{\prime }}{G}\right)\)-expansion technique on this model to obtain a new exact and solitary traveling wave solutions. The propose of this research is applying new method on this models to discover new form of soliton solutions that this makes the study of the electric and magnetic field of these pulses and the extent of their effect in the optical fiber more interesting.