Kinky breathers, multi-peak and multi-wave soliton solutions for the nonlinear propagation of Kundu-Eckhaus dynamical model

The multi-wave solutions for nonlinear Kundu-Eckhaus (KE) equation are obtained using logarithmic transformation and symbolic computation using the function method. Three-wave method, double exponential and homoclinic breather approach are used to get these solutions. We study the conflict between our results and considerably-known results and state that the solutions reached here are new. By specifying the suitable values for the parameter, the drawings of the solutions obtained are shown in this paper.