The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Year 2017, Volume: 2 Issue: 1, 13 - 26, 30.04.2017

Yusuf Pandir , Halime Ulusoy

https://doi.org/10.30931/jetas.303875

https://izlik.org/JA87ZM38EY

Abstract

In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV) equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Keywords

Multi-wave method , generalized forms of 5th order KdV equation , fth order KdV (fKdV) equation , Soliton solutions.

References

• [1] A. Biswas, H. Triki, 1-Soliton solution of the D(m; n) equation with generalized evolution, Appl. Math. Comput. 217 (2011), 8482-8488.
• [2] R. Hirota, Exact solution of the KdV equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194.
• [3] R. Hirota, Exact N-soliton solution of the wave equation of long waves in shallow and nonlinear lattices, J. Math. Phys. 14 (1973), 810-814.
• [4] Y. Gurefe, E. Misirli, Exp-function method for solving nonlinear evolution equations with higher order nonlinearity, Comput. Math. Appl. 61 (2011), 2025-2030.
• [5] E. Misirli, Y. Gurefe, Exp-function method for solving nonlinear evolution equations, Math. Comput. Appl. 16 (2011), 258-266.
• [6] Y. Gurefe, E. Misirli, New variable separation solutions of two-dimensional Burgers system, Appl. Math. Comput. 217 (2011), 9189-9197.
• [7] Y. Gurefe, A. Sonmezoglu, E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Pramana-J. Phys. 77 (2011), 1023-1029.
• [8] Z.D. Dai, C.J. Wang, S.Q. Lin, D.L. Li, G. Mu, The three-wave method for nonlinear evolution equations, Nonl. Sci. Lett. A. 1 (2010), 77-82.
• [9] Y. Shi, Z.D. Dai, S. Han, L. Huang, The multi-wave method for nonlinear evolution equations, Math. Comput. Appl. 15 (2010), 776-783.
• [10] Y. Shi, D. Li, New exact solutions for the (2+1)-dimensional SawadaKotera equation, Comput. Fluids 68 (2012), 88-93.
• [11] Y. Gurefe, Y. Pandir, E. Misirli, New Exact Solutions of Stochastic KdV Equation, Appl. Math. Sci. 6(65) (2012) 3225-3234.
• [12] L. Girgis, A. Biswas, Soliton perturbation theory for nonlinear wave equations, Appl. Math. Comput. 216 (2010), 2226-2231.
• [13] A. Biswas, S. Konar, Soliton perturbation theory for the fth order KdV-type equations with power law nonlinearity, Appl. Math. Lett. 20 (2007), 1122-1125.