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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0701054 (nlin)
[Submitted on 27 Jan 2007]

Title:KP Trigonometric Solitons and an Adelic Flag Manifold

Authors:Luc Haine
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Abstract: We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices satisfying certain rank one conditions. The result can be seen as a non-self-dual illustration of Wilson's fundamental idea [Invent. Math. 133 (1998), 1-41] for understanding the (self-dual) bispectral property of the rational solutions of the KP hierarchy. It also gives a bispectral interpretation of a (dynamical) duality between the hyperbolic Calogero-Moser system and the rational Ruijsenaars-Schneider system, which was first observed by Ruijsenaars [Comm. Math. Phys. 115 (1988), 127-165].
Comments: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at this http URL
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Cite as: arXiv:nlin/0701054 [nlin.SI]
  (or arXiv:nlin/0701054v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0701054
Journal reference: SIGMA 3 (2007), 015, 15 pages
Related DOI: https://doi.org/10.3842/SIGMA.2007.015

Submission history

From: Luc Haine [view email] [via SIGMA proxy]
[v1] Sat, 27 Jan 2007 15:48:31 UTC (19 KB)
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