We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130"

by Elsayed M. E. Zayed, Yasser A. Amer, Reham M. A. Shohib
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 86 - Number 1
Year of Publication: 2014
Authors: Elsayed M. E. Zayed, Yasser A. Amer, Reham M. A. Shohib
10.5120/14952-3114

Elsayed M. E. Zayed, Yasser A. Amer, Reham M. A. Shohib . Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130". International Journal of Computer Applications. 86, 1 ( January 2014), 26-36. DOI=10.5120/14952-3114

@article{ 10.5120/14952-3114,
author = { Elsayed M. E. Zayed, Yasser A. Amer, Reham M. A. Shohib },
title = { Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130" },
journal = { International Journal of Computer Applications },
issue_date = { January 2014 },
volume = { 86 },
number = { 1 },
month = { January },
year = { 2014 },
issn = { 0975-8887 },
pages = { 26-36 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume86/number1/14952-3114/ },
doi = { 10.5120/14952-3114 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:03:06.836559+05:30
%A Elsayed M. E. Zayed
%A Yasser A. Amer
%A Reham M. A. Shohib
%T Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130"
%J International Journal of Computer Applications
%@ 0975-8887
%V 86
%N 1
%P 26-36
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The authors of the above article proposed the improved - expansion method and found some traveling wave solutions for each of two nonlinear evolution equations in mathematical physics, namely the Regularized Long Wave (RLW) equation and the Symmetric Regularized Long Wave (SRLW) equation. In the present article, we have noted that if we use a suitable transformation, the improved (G'/G)-expansion method can be reduced into the well -known generalized Riccati equation mapping method which provides us with much more traveling wave solutions, namely twenty seven solutions for each of these two nonlinear evaluation equations. Comparison between the results of these two methods is presented.

References
  1. Ablowitz M. J. . and Clarkson P. A. 1991. Solitons, nonlinear evolution equations and inverse scattering transform,Cambridge University Press NewYork.
  2. Miura M. R. 1978, Backlund transformation, Springer, Berlin.
  3. Hirota R. Exact solutions of the KdV equation for multiple collisions of solutions. Phys. Rev. Lett, 27(1971) 1192-1194.
  4. Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 277(2000) 212-218.
  5. Wazwaz A. M. A sine- cosine method for handling nonlinear wave equations. Math. Comput. Model 40(2004) 499-508.
  6. He J. H. and Wu X. H. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals, 30(2006) 700-708,.
  7. Zhang S. and Xia T. C. A generalized F-expansion method and new exact solutions of Konopelchenho-Dukrovsky equation. Appl. Math. Comput. 183(2006) 1190-1200.
  8. Lu D. Jacobi elliptic function solutions for two variant Boussinesq equations. Chaos, Solitons and Fractals, 24(2005) 1373–1385.
  9. Wang M. , Li X. and Zhang J. The -eapansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A, 372(2008) 417-423.
  10. Jawad A. J. M. , Petkovic M. D. and Biswas A. , Modified simple equation method for nonlinear evolution equation. Math. Comput. Model, 217(2010) 869-677.
  11. Ma W. X. and Fuchssteiner, Explicit and exact solutions of KPP equation. Int. J. Nonl. Mech. 31(1996) 329-338.
  12. Ma W. X. , Wu H. Y. and He J. S. Partial differential equations possessing Frobenius integrable decompositions. Phys. Lett. A. 364(2007) 29-32.
  13. Ma W. X. and Lee J. H. A transformed rational function method and exact solution to the (3+1)-dimensional Jimbo Miwa equation. Chaos, Solitons and Fractals. 42(2009) 1356-1363.
  14. Ma W. X. , Huang T. and Zhang Y. A multiple exp-function method for nonlinear differentianal equations and its applications. Phys. Scrit 82(2010) 065003.
  15. Ma W. X. Generalized bilinear differential equations. Studies Nonl. Sci. 2 (2011) 140-144.
  16. Ma W. X and Ahu Z. Solving the (3+1)-dimensional generalized KP and BKP by the multiple exp-function algorithm. Appl. Math. Comput. 218(2012) 1171-1179.
  17. Yang A. M. , Yang X. J. and Li Z. B. Local fractional series expansion method for solving wave and diffusion equations on cantor sets. Abst. Appl. Anal. vol 2013 article ID: 351057.
  18. Yang X. J. and Baleanu D. Fractal heat conduction problem solved by local fractional variation iteration method. Thermal Sci. 17(2013) 625-628.
  19. Liu X. , Zhang W. and Li Z. , Application of improved - expansion method to traveling wave solutions of two nonlinear evolution equations, Adv. Appl. Math. Mech. 4(2012) 122-130,
  20. Ding X . F. , Jing C. and Sheng L. Z. Using symbolic computation to exactly solve the integrable Broer-Kaup equations in (2+1)- dimensional spaces. Commu. Theor. Phys. 43(200) 585-590.
  21. Yomba E. The extended Fan Sub-equation method and its application to (2+1) - dimensional dispersive long wave and Whitham- Broer-Kaup equations. Chin. J. Phys. 43(2005) 789-805.
  22. Zhu S. D. The generalized Riccati equation mapping method in nonlinear evolution equation: application to (2+1)-dimensional Boiti-lion-Pempinelle equation. Chaos, Solitons and Fractals, 37(2008) 1335–1342
  23. Li Z. and Zhang X. New exact kink solutions and periodic form solutions for a generalized Zakharov-Kuznetsov equation with variable coefficients, Commu. Nonlinear Sci. Numer. Simula. ,15(2010) 3418-3422.
  24. Zayed E. M. E. and Arnous A. H Many Exact solutions for nonlinear dynamics of DNA model using the generalized Riccati equation mapping method. Sci. Res. Essays. 8 (2013) 340-346.
  25. Zayed E. M. E. , Amer Y. A. and Shohib R. M. A. The improved Riccati equation mapping method for constructing many families of exact solutions for nonlinear partial differential equation of nanobioscience. Int. J. Phys. Sci. 8(2013) 1246-1255.
Index Terms

Computer Science
Information Sciences

Keywords

Improved - expansion method Generalized Riccati equation mapping method the nonlinear RLW equation the nonlinear SRLW equation traveling wave solutions

Powered by PhDFocusTM