Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods

Abstract

The special kind of () G G ′-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.

On the multi-waves, interaction and Peregrine-like rational solutions of perturbed Radhakrishnan–Kundu–Lakshmanan equation

“…Modeling and obtaining solutions to the problems encountered are important for understanding physical phenomena. Many powerful methods have been developed to obtain analytical solutions of NLEEs such as the rational ¢ G G ( )-expansion method [1], the F-expansion method [2], the variational iteration method [3], modified simple equation method [4], the modified auxiliary equation method [5], the Jacobi elliptic function rational expansion method [6], and extended modified direct algebraic method, extended mapping method and Seadawy techniques to find solutions for some nonlinear PDEs [7][8][9][10][11][12][13]. However, NLEEs are also used in the modeling of the dynamics of the soliton propagation via any optical wave guide [14] .…”