Constructing new wave solutions to the $$(2 + 1)$$-dimensional Davey–Stewartson equation (DSE) which arises in fluid dynamics

Abstract

In this paper, we utilize the uniform algebraic method and construct some new wave solutions to the (2 + 1)-dimensional Davey-Stewartson equation which arises in fluid dynamics. We successfully obtain some hyperbolic and trigonometric function solutions to this equation. Subsequently, We have also built the Lagrangian and the Hamiltonian for the second-order nonlinear ODE corresponding to the traveling wave reduction of the (DSE)-equation. Moreover, we plot 2D and 3D surfaces representing the obtained solutions by considering some suitable values of the parameters. The unique (2 + 1)-dimensional dynamics of the obtained exact solutions of the (DSE) equation may help to understand the formation and key properties of traveling waves in many other physical settings. Before the end of this paper, we compare our results with the existing results in the literature by presenting comprehensive conclusions.

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

“…For example, the solutions of the DDSEs might explain the interaction of a properly matched spatiotemporal optical pattern and microwaves. As a result, many authors have investigated the analytical solutions for this equation by using different methods such as the extended Jacobi's elliptic function [31], the first integral method [32], the trial equation method [33], the uniform algebraic method [34], the double exp-function [35], generalized (G /G)-expansion [36], (G /G)-expansion [37] and sine-cosine [38].…”