Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
نویسنده
چکیده
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 the same as commutative ones as well. Noncommutative toroidal Gelfand-Dickey hierarchy is also introduced and the exact multi-soliton solutions are given. The author visits Oxford from 16 August, 2005 to 15 December, 2006. E-mail: [email protected], [email protected]
منابع مشابه
Noncommutative Solitons and Integrable Systems *
We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter part is a report on recent results of existence of infinite conserved densities and exact multi-soliton solutions for noncommutative Gelfand-Dickey hierarchies....
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