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

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.