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High Energy Physics - Theory

arXiv:hep-th/0309265 (hep-th)
[Submitted on 30 Sep 2003 (v1), last revised 11 Dec 2003 (this version, v2)]

Title:Towards Noncommutative Integrable Equations

Authors:Masashi Hamanaka, Kouichi Toda
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Abstract: We study the extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by the Lax-pair generating technique and the Sato theory. The Sato theory has revealed essential aspects of the integrability of commutative soliton equations and the noncommutative extension is worth studying. We succeed in deriving various noncommutative hierarchy equations in the framework of the Sato theory, which is brand-new. The existence of the hierarchy would suggest a hidden infinite-dimensional symmetry in the noncommutative Lax equations. We finally show that a noncommutative version of Burgers equation is completely integrable because it is linearizable via noncommutative Cole-Hopf transformation. These results are expected to lead to the completion of the noncommutative Sato theory.
Comments: 14 pages, LaTeX, talk given by K.T. at the fifth international conference on Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, 23-29 June 2003; v2: accepted for publication in the proceedings, typos corrected, references added
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
Report number: UT-Komaba/03-17
Cite as: arXiv:hep-th/0309265
  (or arXiv:hep-th/0309265v2 for this version)
  https://doi.org/10.48550/arXiv.hep-th/0309265
Journal reference: EconfC0306234:404-411,2003

Submission history

From: Masashi Hamanaka [view email]
[v1] Tue, 30 Sep 2003 11:23:28 UTC (12 KB)
[v2] Thu, 11 Dec 2003 05:44:08 UTC (13 KB)
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