Generalized self-dual Yang-Mills flows, explicit solutions and reductions

Abstract

An evolution equation is added to the generalized self-dual Yang—equations. The evolution equation contains terms of negative powers of the spectral parameter as well as terms of positive powers. The Darboux matrix method is used to obtain explicit solutions, especially single and multiple solitons. All integrable soliton equations in the framework of AKNS system (in R n+ 1 or R 1+1) can be derived from the generalized Yang—Mills flows by reduction.