Some new integrable equations from the self-dual Yang-Mills equations

TL;DR

This paper derives new integrable equations in lower dimensions from the self-dual Yang-Mills equations using symmetry reductions, expanding the class of known integrable systems with explicit Lax pairs.

Contribution

It introduces several new nonautonomous integrable equations obtained via symmetry reductions of SDYM equations, with explicit Lax pairs provided.

Findings

New nonautonomous integrable equations derived from SDYM

Explicit Lax pairs constructed for all new equations

Connections established between SDYM and various classical integrable systems

Abstract

Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are nonautonomous versions of the chiral model in (2+1) dimensions, generalized nonlinear Schrodinger, Korteweg-de Vries, Toda lattice, Garnier and Euler-Arnold equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations.