On Solving the (2+1)-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau Equation Using Five Different Techniques

Elsayed M. E. Zayed; A. G. Al-Nowehy; Mona E. M. Elshater

doi:10.4208/jpde.v31.n2.1

Authors

Elsayed M. E. Zayed Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt
A. G. Al-Nowehy Mathematics Department, Faculty of Education and Science, Taiz University, Taiz, Yemen
Mona E. M. Elshater Mathematics Department, Faculty of Sciences, Zagazig University, P. O. Box 44519, Zagazig, Egypt

DOI:

https://doi.org/10.4208/jpde.v31.n2.1

Keywords:

(G′/G)-expansion method;auxiliary equation method;modified simple equation method;first integral method;Riccati equation method;exact traveling wave solutions;solitary wave solutions;Cubic-quintic Ginzburg-Landau equation.

Abstract

In this article, we apply five different techniques, namely the (G′/G)-expansion method, an auxiliary equation method, the modified simple equation method, the first integral method and the Riccati equation method for constructing many new exact solutions with parameters as well as the bright-dark, singular and other soliton solutions of the (2+1)-dimensional nonlinear cubic-quintic Ginzburg-Landau equation. Comparing the solutions of this nonlinear equation together with each other are presented. Comparing our newresults obtained in this articlewith thewell-known results are given too.