Exact solutions and excitations for the Davey-Stewartson equations with nonlinear and gain terms

TL;DR

This paper derives explicit solutions and novel excitations for the (2+1)-dimensional Davey-Stewartson equations with nonlinear and gain terms, providing insights into their features and potential applications to related equations like the nonlinear Schrödinger equation.

Contribution

It introduces a variable separation approach to find exact solutions and excitations for the DS equations, extending understanding of their dynamics and applicability.

Findings

Derived explicit solutions for DS equations with gain and nonlinear terms

Identified novel excitations and their features

Predicted similar solutions in related equations like nonlinear Schrödinger

Abstract

We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS equations, and further demonstrate different features of these excitations. More importantly, the similar solutions and excitations can be predicted to exist in other related revolution equations such as nonlinear Schr\"odinger equation to explain the Bose-Einstein condensation.