Novel analytical simulations of the complex nonlinear Davey–Stewartson equations in the gravity-capillarity surface wave packets

Abstract

This article investigates the analytical wave solutions of the complex nonlinear Davey–Stewartson (CNLDS) equations by employing two novel analytical schemes. These equations are considered as the main icon in describing the water waves in the gravity-capillarity surface wave packets. These equations have been derived by Davey and Stewartson for the first time as a higher-general dimensional model of the well-known model Schrödinger equation. The extended exponential function (EEF) and the Khater II methods are employed to construct novel solutions. The obtained solutions are plotted in different techniques for illustrating the dynamical behavior of the water waves. Additionally, The obtained results’ stability is checked. The obtained results’ novelty is explained by comparing our solutions and published results in recent studies.