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

Chaudry Masood Khalique and Karabo Plaatjie
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Chaudry Masood Khalique: 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
Karabo Plaatjie: 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

Mathematics, 2021, vol. 9, issue 12, 1-17

Abstract: 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.

Keywords: two-dimensional generalized shallow water wave equation; Lie point symmetries; Kudryashov’s method; conservation laws; Noether’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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