AM  Vol.5 No.6 , April 2014
New Applications to Solitary Wave Ansatz
ABSTRACT

In this article, the solitary wave and shock wave solitons for nonlinear Ostrovsky equation and Potential Kadomstev-Petviashvili equations have been obtained. The solitary wave ansatz is used to carry out the solutions.



Cite this paper
Younis, M. and Ali, S. (2014) New Applications to Solitary Wave Ansatz. Applied Mathematics, 5, 969-974. doi: 10.4236/am.2014.56092.
References
[1]   Johnson, R.S. (1970) A Non-Linear Equation Incorporating Damping and Dispersion. Journal of Fluid Mechanics, 42, 49-60.
http://dx.doi.org/10.1017/S0022112070001064

[2]   Glockle, W.G. and Nonnenmacher, T.F. (1995) A Fractional Calculus Approach to Self Similar Protein Dynamics. Biophysical Journal, 68, 46-53.
http://dx.doi.org/10.1016/S0006-3495(95)80157-8

[3]   Podlubny, I. (1999) Fractional Differential Equations. Academic Press, San Diego.

[4]   He, J.H. (1999) Some Applications of Nonlinear Fractional Differential Equations and Their Applications. Bulletin of Science and Technology, 15, 86-90.

[5]   Younis, M., Zafar, A., Ul-Haq, K. and Rahman, M. (2013) Travelling Wave Solutions of Fractional Order Coupled Burgers Equations by -Expansion Method. American Journal of Computational and Applied Mathematics, 3, 81-85.

[6]   Younis, M. and Zafar, A. (2014) Exact Solution to Nonlinear Differential Equations of Fractional Order via (G'/G)-Expansion Method. Applied Mathematics, 5, 1-6.
http://dx.doi.org/10.4236/am.2014.51001

[7]   Younis, M. (2013) The First Integral Method for Time-Space Fractional Differential Equations. Journal of Advanced Physics, 2, 220-223.
http://dx.doi.org/10.1166/jap.2013.1074

[8]   Wang, Q. (2006) Numerical Solutions for Fractional KDV-Burgers Equation by Adomian Decomposition Method. Applied Mathematics and Computation, 182, 1048-1055.
http://dx.doi.org/10.1016/j.amc.2006.05.004

[9]   Liu, J. and Hou, G. (2011) Numerical Solutions of the Spaceand Time-Fractional Coupled Burgers Equations by Generalized Differential Transform Method. Applied Mathematics and Computation, 217, 7001-7008.
http://dx.doi.org/10.1016/j.amc.2011.01.111

[10]   Liu, S.K., Fu, Z.T., Liu, S.D. and Zhao, Q. (2001) Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Nonlinear Wave Equations. Physics Letters A, 289, 69-74.
http://dx.doi.org/10.1016/S0375-9601(01)00580-1

[11]   Parkes, E.J. and Duffy, B.R. (1996) An Automated Tanh-Function Method for Finding Solitary Wave Solutions to Non-Linear Evolution Equations. Computer Physics Communications, 98, 288-300.
http://dx.doi.org/10.1016/0010-4655(96)00104-X

[12]   Younis, M. and Zafar, A. (2013) The Modified Simple Equation Method for Solving Nonlinear Phi-Four Equation. International Journal of Innovation and Applied Studies, 2, 661-664.

[13]   Triki, H. and Wazwaz, A.-M. (2011) Dark Solitons for a Combined Potential KdV and Schwarzian KdV Equations with t-Dependent Coefficients and Forcing Term. Applied Mathematics and Computation, 217, 8846-8851.
http://dx.doi.org/10.1016/j.amc.2011.03.050

[14]   Bekir, A., Aksoy, E. and Guner, O. (2012) Bright and Dark Soliton Solitons for Variable Cefficient Diffusion Reaction and Modified KdV Equations. Physica Scripta, 85, 35009-35014.
http://dx.doi.org/10.1088/0031-8949/85/03/035009

 
 
Top