Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics

Karabo Plaatjie¹  Chaudry Masood Khalique¹ 

[1] International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa;

关键词: two-dimensional generalized shallow water wave equation;    Lie point symmetries;    Kudryashov’s method;    conservation laws;    Noether’s theorem;   

DOI  :  10.3390/math9121439

来源: DOAJ

【 摘 要 】

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

【 授权许可】

Unknown