Notes on exact multi-soliton solutions of noncommutative integrable hierarchies
نویسندگان
چکیده
منابع مشابه
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
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 co...
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Some direct relations between soliton solutions of integrable hierarchies and thermodynamical quantities of the Coulomb plasmas on the plane are revealed. We find that certain soliton solutions of the Kadomtsev-Petviashvili (KP) and B-type KP (BKP) hierarchies describe two-dimensional one or two component plasmas at special boundary conditions and fixed temperatures. It is shown that different ...
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We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special “vacuum solutions” such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those “vacuum solitons” by the dressing transformation procedure. This talk is concerned with t...
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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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The Darboux–Dressing Transformations developed in [1] are here applied to construct soliton solutions for a class of boomeronic–type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one soliton solutions. The formulae are specialised to the particularly interesting case of the resonant interaction of three waves, a well-known model wh...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2007
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2007/02/094