The U(N) chiral model and exact multi-solitons

Abstract

We use a binary Darboux transformation to obtain exact multisoliton solutions of the principal chiral model and its noncommutative generalization. We also show that the exact multisolitons of the noncommutative principal chiral model in two dimensions and noncommutative (anti) self dual Yang Mills equations in four dimensions can be expressed explicitly in terms of quasi-determinants.