The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources

TL;DR

This paper introduces and solves non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources, providing explicit quasideterminant solutions and novel reductions.

Contribution

It establishes the equations with self-consistent sources and derives their exact quasideterminant solutions, including the first construction of a matrix sine-Gordon equation with such sources.

Findings

Two families of quasideterminant solutions for the Toda lattice with sources.

First-time construction of a matrix sine-Gordon equation with self-consistent sources.

Explicit quasideterminant solutions for the new equations.

Abstract

The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources are established and solved. Two families of quasideterminant solutions are presented for the non-Abelian two-dimensional Toda lattice with self-consistent sources. By employing periodic and quasi-periodic reductions, a matrix sine-Gordon equation with self-consistent sources is constructed for the first time, for which exact solutions in terms of quasideterminants are derived.