Exact Solutions for Generalized (3+1)-Dimensional Shallow Water-Like (SWL) Equation

Year 2019, Volume: 2 Issue: 1, 55 - 57, 30.10.2019

Faruk Düşünceli

Abstract

In this paper, we demonstrate the exact solutions of the generalized (3+1)-dimensional shallow water-like (SWL) equation by using Bernoulli sub-equation function method. Some new solutions are successfully constructed. We carried out all the computations by Wolfram Mathematica.

Keywords

Generalized (3+1) shallow water-like (SWL) equation, Bernoulli sub-equation function method

References

• [1] Y. Zhang, H. Dong, X. Zhang, and H. Yang, “Rational solutions and lump solutions to the generalized (3+1)-dimensional Shallow Water-like equation,” Computers & Mathematics with Applications, vol. 73, no. 2, pp. 246–252, 2017.
• [2] Y.-N. Tang, W.-X. Ma, and W. Xu, “Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation,” Chinese Physics B, vol. 21, no. 7, 2012.
• [3] B. Tian and Y.-T. Gao, “Beyond travelling waves: A new algorithmfor solving nonlinear evolution equations,” Computer Physics Communications, vol. 95, no. 2-3, pp. 139–142, 1996.
• [4] E. Zayed, “travelling wave solutions for higher dimensional nonlinear evaluation equations using G’/G expansion method,” Journal of Applied Mathematics & Informatics, vol. 28, no. 1, 2, pp. 383–395, 2010.
• [5] R. Sadat, M. Kassem, and Wen-Xiu Ma, “Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model,” Advances in Mathematical Physics, vol. 2018, Article ID 9178480, 8 pages, 2018.
• [6] Haci Mehmet Baskonus, Hasan Bulut and Dilara Gizem Emir, Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method, Mathematics Letters, 1(1), 1-9, 2015.
• [7] B. Zheng, Application of A generalized Bernoulli Sub-ODE Method for finding traveling Solutions of Some Nonlinear Equations, WSEAS Transactions on Mathematics, 7(11),618-626,2012.