The Traveling Wave Solutions for Some Nonlinear PDEs in Mathematical Physics
Khaled A. Gepreel, Saleh Omran, Sayed K. Elagan
.
DOI: 10.4236/am.2011.23040   PDF   HTML     5,800 Downloads   12,308 Views   Citations

Abstract

In the present article, we construct the exact traveling wave solutions of some nonlinear PDEs in the mathematical physics via (1 + 1) dimensional Kaup Kupershmit equation, the (1 + 1) dimensional seventh order KdV equation and (1 + 1) dimensional Kersten-Krasil Shchik equations by using the modified truncated expansion method. New exact solutions of these equations are found.

Share and Cite:

K. Gepreel, S. Omran and S. Elagan, "The Traveling Wave Solutions for Some Nonlinear PDEs in Mathematical Physics," Applied Mathematics, Vol. 2 No. 3, 2011, pp. 343-347. doi: 10.4236/am.2011.23040.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Weiss, M. Tabor and G. Carnevalle, “The Painleve Property for Partial Differential Equations,” Journal of Mathematical Physics, Vol. 24, No. 3, 1983, pp. 522-526. doi:10.1063/1.525721
[2] N. A. Kudryashov, “Exact Soliton Solutions of the Generalized Evolution Equation of Wave Dynamics,” Journal of Applied Mathematics and Mechanics, Vol. 52, No. 3, 1988, pp. 361-365. doi:10.1016/0021-8928(88)90090-1
[3] J. Weiss, “The Panleve Property for Partial Differential Equations. II: Backlund Transformation, Lax Pairs, and the Schwarzian Derivative,” Journal of Mathematical Physics, Vol. 24, No. 6, 1983, pp. 1405-1413. doi:10.1063/1.525875
[4] N. A. Kudryashov, “Exact Solutions of the Generalized Kuramoto—Sivashinsky Equation,” Physics Letters A, Vol. 147, No. 5-6, 1990, pp. 287-291. doi:10.1016/0375-9601(90)90449-X
[5] N. A. Kudryashov and N. B. Loguinova, “Extended Simpliest Equation Method for Nonlinear Differential Equations,” Applied Mathematics and Computation, Vol. 205, No. 1, 2008, pp. 396-402. doi:10.1016/j.amc.2008.08.019
[6] E. J. Parkes and B. R. Duffy, “An Automated Tanh-function Method for Finding Solitary Wave Solutions to Nonlinear Evolution Equations,” Computer Physics Communications, Vol. 98, No. 3, 1996, pp. 288-300. doi:10.1016/0010-4655(96)00104-X
[7] N. A. Kudryashov and M. V. Demina, “Polygons of Differential Equations for Finding Exact Solutions,” Chaos, Solitons & Fractals, Vol. 33, No. 5, 2007. pp. 1480-1496. doi:10.1016/j.chaos.2006.02.012
[8] P. A. Clarkson and M. D. Kruskal, “New Similarity Reductions of the Boussinesq Equation,” Journal of Mathematical Physics, Vol. 30, No. 10, 1989, pp. 2201-2213. doi:10.1063/1.528613
[9] P. N. Ryabov, “Exact Solutions of the Kudryashov-Sinelshchikov Equation,” Applied Mathematics and Computation, Vol. 217, No. 7, 2010, pp. 3585-3590. doi:10.1016/j.amc.2010.09.003
[10] N. A. Kudryashov, “Analytical Theory of Nonlinear Differential Equations,” Institute of Computer Investigations, Moscow, 2004.
[11] M. Musette and C. Verhoeven, “Nonlinear Superposition Formula for the Kaup-Kupershmidt Partial Differential Equation,” Physica D, Vol. 144, No. 1-2, 2000, pp. 211-220. doi:10.1016/S0167-2789(00)00081-6
[12] A. H. Salas, “Computing Exact Solutions to a Generalized Lax Seventh-Order Forced KdV Equation,” Applied Mathematics and Computation, Vol. 216, No. 8, 2010, pp. 2333-2338. doi:10.1016/j.amc.2010.03.078
[13] E. M. E. Zayed and K. A. Gepreel, “New Applications of an Improved(G′/G)-Expansion Method to Constract the Exact Solutions of Nonlinear PDEs,” International Journal of nonlinear Science and Numerical Simulation, Vol. 11, No. 4, 2010, pp. 273-283.
[14] A. K. Kalkanli, S. Y. Sakovich and T. Yurdusen, “Integrability of Kersten-Krasil’shchik Coupled KdV-mKdV Equations: Singularity Analysis and Lax Pair,” Journal of Mathematical Physics, Vol. 44, No. 4, 2003, pp. 1703-1708. doi:10.1063/1.1558903

Copyright © 2021 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.