Non-commutative multi-solitons in 2+1 dimensions

Abstract

The study of non-commutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2 + 1 dimensions we employ the dressing method to construct explicit multi-soliton configurations on non-commutative R2,1 . These solutions, abelian and non-abelian, feature exact time-dependence for any value of the noncommutativity parameter θ and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.