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New Applications to Solitary Wave Ansatz
Centre for Undergraduate Studies, University of the Punjab, Lahore, Pakistan
Department of Mathematics, Minhaj University, Lahore, Pakistan
- 1 Centre for Undergraduate Studies, University of the Punjab, Lahore, Pakistan
- 2 Department of Mathematics, Minhaj University, Lahore, Pakistan
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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.
KeywordsSolitary Wave SolitonsShock Wave SolitonsThe Ostrovsky EquationThe Potential Kadomstev-Petviashvili EquationSolitary Wave Ansatz
- 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
- 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
- Podlubny, I. (1999) Fractional Differential Equations. Academic Press, San Diego.
- He, J.H. (1999) Some Applications of Nonlinear Fractional Differential Equations and Their Applications. Bulletin of Science and Technology, 15, 86-90.
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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