On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain

TL;DR

This paper presents a new method for explicitly constructing solutions to the Davey--Stewartson I equation using a dressing chain linked to the Toda lattice associated with the Lie algebra A2, introducing solutions with two arbitrary functions.

Contribution

It introduces a novel dressing chain approach based on the Toda lattice for solving the DS I equation, expanding the class of explicit solutions with arbitrary functions.

Findings

Constructed a new class of explicit solutions for DS I.

Demonstrated the use of the A2 Toda lattice as a dressing chain.

Provided solutions with two arbitrary functions.

Abstract

An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new class of explicit solutions is constructed, containing freedom in two arbitrary functions. In this case the generalized Toda lattice corresponding to the simple Lie algebra $A_2$ is used as a dressing chain.