Volume 31, Issue 2
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

J. Part. Diff. Eq., 31 (2018), pp. 97-118.

Published online: 2018-07

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  • 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.

  • 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.

  • AMS Subject Headings

35C05 35K99 35P05 35P99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

eme_zayed@yahoo.com (Elsayed M. E. Zayed)

alnowehy2010@yahoo.com (A. G. Al-Nowehy)

mona_el.shater@yahoo.com (Mona E. M. Elshater)

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@Article{JPDE-31-97, author = {Zayed , Elsayed M. E. and Al-Nowehy , A. G. and Elshater , Mona E. M. }, title = {On Solving the (2+1)-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau Equation Using Five Different Techniques}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {2}, pages = {97--118}, 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/12513.html} }
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