A new multi-component two dimensional Toda lattice hierarchy and two dimensional Toda lattice with self-consistent sources

TL;DR

This paper introduces a new multi-component two-dimensional Toda lattice hierarchy that encompasses the 2D Toda lattice with self-consistent sources, providing Lax representations and a Darboux transformation for solution generation.

Contribution

It proposes a novel multi-component hierarchy including the 2D Toda lattice with sources, along with Lax representations and a Darboux transformation for solution construction.

Findings

Established a new hierarchy including 2dTLSCS

Derived Lax representations for the hierarchy

Constructed a Darboux transformation for solutions

Abstract

We propose a new multi-component two-dimensional Toda lattice hierarchy (mc2dTLH) which includes two-dimensional Toda lattice equation with self-consistent sources (2dTLSCS) as the first non-trivial equation. The Lax representations for this mc2dTLH are presented. We construct a non-auto-B\"acklund Darboux transformation (DT) for 2dTLSCS by applying the method of variation of constant (MVC) to ordinary DT of 2dTLSCS. This non-auto-B\"acklund DT enables us to obtain various solutions such as solitons, rational solutions etc., to 2dTLSCS.