Author(s)

Longmin Dong, Zhu Guo, Yinghui He

Department of Mathematics, Honghe University, Mengzi, China.

In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended F-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.

Shallow Water Wave Equations, Nonlinear Wave Solution, Lie Symmetry Analysis, Extended F-Expansion Method

Dong, L. , Guo, Z. and He, Y. (2020) Some New Nonlinear Wave Solutions for a Higher-Dimensional Shallow Water Wave Equation. Journal of Applied Mathematics and Physics, 8, 1845-1860. doi: 10.4236/jamp.2020.89139.