Noncommutative Multi-Solitons in 2+1 Dimensions

Abstract

The study of noncommutative 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 noncommutative R^{2,1}. These solutions, abelian and nonabelian, feature exact time-dependence for any value of the noncommutativity parameter theta and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.

1+24 pages, no figures; v2: minor corrections, two references added; v3: typos corrected

References in corpus (5)

• Exact Noncommutative KP and KdV Multi-solitons
• Seiberg-Witten Transforms of Noncommutative Solitons
• A tour through N=2 strings
• Noncommutative Generalized NS and Super Matrix KdV Systems from a Noncommutative Version of (Anti-) Self-Dual Yang-Mills Equations
• Mathematics and Physics of N=2 Strings

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