Stability analysis, symmetry solutions and conserved currents of a two-dimensional extended shallow water wave equation of fluid mechanics

Abstract

This paper analytically investigates a new (2+1)-dimensional extended shallow water wave equation. Lie group theory along with direct integration is used to achieve some solutions of the equation. The solutions obtained are in terms of Jacobi elliptic function as well as Weierstrass elliptic function. Besides, we apply the He’s variational technique to secure some non-topological soliton solutions of the equation. Series solution of the equation is also achieved by employing power series technique and we show the convergence of the series. Furthermore, graphical exhibitions of the dynamical character of the gained result are presented and discussed in a bid to have a sound understanding of the physical phenomena of the underlying model. In addition, we examine the stability analysis of the equation. Conclusively, we give the conserved currents of the aforementioned equation by employing the homotopy formula together with the Noether theorem.

Keywords

• Two-dimensional extended shallow water wave equation
• Lie group theory
• Exact solutions
• Power series
• He’s variational technique
• Conserved currents