Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

Abstract

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.

18 pages, v3: references added, version to appear in JHEP

References in corpus (2)

• Noncommutative Ward's Conjecture and Integrable Systems
• On the structure of $(2+1)$--dimensional commutative and noncommutative integrable equations

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• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields