Quadratic-Argument Approach to the Davey-Stewartson Equations

TL;DR

This paper introduces a quadratic-argument method to find exact solutions to the Davey-Stewartson equations, which model long-term surface wave evolution, by leveraging symmetry transformations.

Contribution

It presents a novel quadratic-argument approach for deriving exact solutions to the Davey-Stewartson equations, expanding the solution space using symmetry transformations.

Findings

Derived various exact solutions using the quadratic-argument method

Identified symmetry transformations applicable to the solutions

Enhanced understanding of wave evolution dynamics

Abstract

The Davey-Stewartson equations are used to describe the long time evolution of a three-dimensional packets of surface waves. Assuming that the argument functions are quadratic in spacial variables, we find in this paper various exact solutions modulo the most known symmetry transformations for the Davey-Stewartson equations.