Share This Article:

Auto-Bäcklund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation

Abstract Full-Text HTML XML Download Download as PDF (Size:1554KB) PP. 215-223
DOI: 10.4236/ajcm.2015.52018    2,590 Downloads   2,952 Views   Citations

ABSTRACT

In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

El-Shiekh, R. (2015) Auto-Bäcklund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation. American Journal of Computational Mathematics, 5, 215-223. doi: 10.4236/ajcm.2015.52018.

References

[1] Bansal A. and Gupta, R.K. (2012) Lie Point Symmetries and Similarity Solutions of the Time-Dependent Coefficients Calogero-Degasperis Equation. Physica Scripta, 86, 035005.
http://dx.doi.org/10.1088/0031-8949/86/03/035005
[2] Wazwaz, A.M. (2008) New Solutions of Distinct Physical Structures to High-Dimensional Nonlinear Evolution Equations. Applied Mathematics and Computation, 196, 363-370.
http://dx.doi.org/10.1016/j.amc.2007.06.002
[3] Peng, Y. (2006) New Types of Localized Coherent Structures in the Bogoyavlenskii-Schiff Equation. International Journal of Theoretical Physics, 45, 1764-1768.
http://dx.doi.org/10.1007/s10773-006-9139-7
[4] Bruzon, M.S., Gandarias, M.L., Muriel, C., Ramierez, J., Saez, S. and Romero, F.R. (2003) The Calogero-Bogoyav-lenskii-Schff Equation in (2 + 1) Dimensions. Journal of Theoretical and Mathematical Physics, 137, 1367-1377.
[5] Wazwaz, A.M. (2008) Multiple-Soliton Solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF Equation. Applied Mathematics and Computation, 203, 592-597.
[6] Moatimid G.M., El-Shiekh R.M. and A.-G. A.A.H. Al-Nowehy (2013) Exact Solutions for Calogero-Bogoyavlenskii-Schiff Equation Using Symmetry Method. Applied Mathematics and Computation, 220, 455-462.
[7] Fan, E. (2000) Two New Applications of the Homogeneous Balance Method. Physics Letter A, 265, 353-357.
http://dx.doi.org/10.1016/S0375-9601(00)00010-4
[8] Fan, E. (2002) Auto-Bäcklund Transformation and Similarity Reductions for General Variable Coefficient KdV Equations. Physics Letter A, 294, 26-30.
[9] Moussa, M.H.M. and El Shikh, R.M. (2008) Auto-Bäcklund Transformation and Similarity Reductions to the Variable Coefficients Variant Boussinesq System. Physics Letter A, 372, 1429-1434.
[10] Moussa, M.H.M. and El Shikh, R.M. (2009) Two Applications of the Homogeneous Balance Method for Solving the Generalized Hirota-Satsuma Coupled KdV System with Variable Coefficients. International Journal of Nonlinear Sci-ence, 7, 29-38.
[11] Hang, Y. and Shang, Y.D. (2012) The Bäcklund Transformations and Abundant Exact Explicit Solutions for a General Nonintegrable Nonlinear Convection-Diffusion Equation. Abstract and Applied Analysis, 2012, 1-11.
http://dx.doi.org/10.1155/2012/489043
[12] El Shiekh, R.M. and Al-Nowehy, A.-G. (2013) Integral Methods to Solve the Variable Coefficient Nonlinear Schrö-dinger Equation. Zeitschrift für Naturforschung, 68a, 255-260.
http://dx.doi.org/10.5560/ZNA.2012-0108
[13] El Shiekh, R.M. (2015) Direct Similarity Reduction and New Exact Solutions for the Variable-Coefficient Kadomtsev-Petviashvili Equation. Zeitschrift für Naturforschung A, 70, 445-450.
http://dx.doi.org/10.1515/zna-2015-0057
[14] El-Wakil, S.A., Abdou, M.A. and Hendi, A. (2008) New Periodic and Soliton Solutions of Nonlinear Evolution Equations. Applied Mathematics and Computation, 197, 497-506.
http://dx.doi.org/10.1016/j.amc.2007.08.090
[15] Veksler, A. and Zarmi, Y. (2005) Wave Interactions and the Analysis of the Perturbed Burgers Equation. Physica D: Nonlinear Phenomena, 211, 57-73.
http://dx.doi.org/10.1016/j.physd.2005.08.001
[16] Yu, X., Gao, Y.-T., Sun, Z.-Y. and Liu, Y. (2010) N-Soliton Solutions, Bäcklund Transformation and Lax Pair for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation. Physica Scripta, 81, 045402.
http://dx.doi.org/10.1088/0031-8949/81/04/045402
[17] Jaradat, H.M., Al-Shara, S., Awawdeh, F. and Alquran, M. (2012) Variable Coefficient Equations of the Kadomtsev-Petviashvili Hierarchy: Multiple Soliton Solutions and Singular Multiple Soliton Solutions. Physica Scripta, 85, Article ID: 035001.
http://dx.doi.org/10.1088/0031-8949/85/03/035001

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.