Soliton Scattering in Noncommutative Spaces

Abstract

We discuss exact multi-soliton solutions to integrable hierarchies on noncommutative space-times in diverse dimension. The solutions are represented by quasi-determinants in compact forms. We study soliton scattering processes in the asymptotic region where the configurations could be real-valued. We find that the asymptotic configurations in the soliton scatterings can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized lump of energy and each solitary wave-packet lump preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. As new results, we present multi-soliton solutions to noncommutative anti-self-dual Yang-Mills hierarchy and discuss 2-soliton scattering in detail.

arXiv comment23 pages; version to appear in Theor. Math. Phys

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Cited by in corpus (4)

• Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• New Soliton Solutions of Anti-Self-Dual Yang-Mills equations
• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields
• Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions