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.
Highlights
Generalized Shallow Water WaveIt is widely known that most physical phenomena of the natural world are governed by nonlinear partial differential equations (NPDEs)
Such equations arise in several physical and other problems such as in the study of electromagnetism, electrodynamics, fluid flow, elasticity, propagation of heat or sound, quantum mechanics, meteorology, and oceanography, just to mention a few. Some of these models include the modified Zakharov–Kuznetsov model [1] that recounts the ion-acoustic drift solitary waves existing in a magnetoplasma with electron–positron ions, which are found in a primordial universe
They can be utilized in constructing solutions of partial differential equations (PDEs) by reducing their order
Summary
It is widely known that most physical phenomena of the natural world are governed by nonlinear partial differential equations (NPDEs). These groups have had an intense impact on pure and applied mathematics in addition to engineering, physics, and other applied sciences It provides the most effective and powerful techniques for obtaining closed-form solutions to NPDEs. For example, see [26,27,28,29,30,31,32,33]. The accuracy of numerical solution methods can be checked by invoking conservation laws They can be utilized in constructing solutions of partial differential equations (PDEs) by reducing their order. In [56], the authors obtained breather-type and analytic soliton solutions of (4) by utilizing Hirota’s bilinear method and the extended homoclinic test technique.
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