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.
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