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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

DOI: 10.4208/jpde.v31.n2.1

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

e.m.e.zayed@hotmail.com (Elsayed M. E. Zayed)

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

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

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-97, author = {Zayed , Elsayed M. E.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} }
TY - JOUR T1 - On Solving the (2+1)-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau Equation Using Five Different Techniques AU - Zayed , Elsayed M. E. AU - Al-Nowehy , A. G. AU - Elshater , Mona E. M. JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 118 PY - 2018 DA - 2018/07 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n2.1 UR - https://global-sci.org/intro/article_detail/jpde/12513.html KW - (G′/G)-expansion method KW - auxiliary equation method KW - modified simple equation method KW - first integral method KW - Riccati equation method KW - exact traveling wave solutions KW - solitary wave solutions KW - Cubic-quintic Ginzburg-Landau equation. AB -

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.

Elsayed M. E. Zayed, A. G. Al-Nowehy & Mona E. M. Elshater. (2019). On Solving the (2+1)-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau Equation Using Five Different Techniques. Journal of Partial Differential Equations. 31 (2). 97-118. doi:10.4208/jpde.v31.n2.1
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