Abstract
In this research, we study exact and solitary traveling solutions of the Kundu–Eckhaus equation with variable coefficients and its relation with famous Schrödinger equation and the complex Burgers equation. Nonlinear complex fractional Kundu–Eckhaus equation has vital role in description of the propagation of the ultra-short femtosecond pulses in an optical fiber. This model has a vital role in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics. We apply a new auxiliary equation method and novel G′G-expansion method on this model to get new exact and solitary traveling wave solutions. The aim of these solutions is showing the slowly varying amplitude of the pulse envelope and discover new physical properties of ultra-short femto second pulses and that happened by using the new from of soliton solutions which obtained by mentioned methods.
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