Multi-soliton solutions of the two-dimensional matrix Davey-Stewartson equation

TL;DR

This paper derives explicit multi-soliton solutions for the (1+2)-dimensional matrix Davey-Stewartson equation using solutions from the matrix Toda chain and linear Schrödinger equations, advancing understanding of complex wave interactions.

Contribution

It provides a novel explicit construction of multi-soliton solutions for the matrix Davey-Stewartson equation based on integrable systems techniques.

Findings

Explicit m-soliton solutions expressed via linear Schrödinger equations.

Connection established between matrix Toda chain solutions and Davey-Stewartson solutions.

Enhances analytical tools for studying multi-dimensional integrable equations.

Abstract

We explicitly obtain the $m$-soliton solutions of the (1+2)-dimensional matrix Davey-Stewartson equation from the known general solution of the matrix Toda chain with fixed ends. We write these solutions in terms of $m+m$ independent solutions of a pair of linear Shr\"odinger equations with Hermitian potentials.