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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 015, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.015
(Mi sigma141)
 

This article is cited in 12 scientific papers (total in 12 papers)

KP Trigonometric Solitons and an Adelic Flag Manifold

Luc Haine

Department of Mathematics, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium
References:
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].
Keywords: Calogero–Moser type systems; bispectral problems.
Received: November 22, 2006; in final form January 5, 2007; Published online January 27, 2007
Bibliographic databases:
Document Type: Article
MSC: 35Q53; 37K10
Language: English
Citation: Luc Haine, “KP Trigonometric Solitons and an Adelic Flag Manifold”, SIGMA, 3 (2007), 015, 15 pp.
Citation in format AMSBIB
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\by Luc Haine
\paper KP Trigonometric Solitons and an Adelic Flag Manifold
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\vol 3
\papernumber 015
\totalpages 15
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  • https://www.mathnet.ru/eng/sigma/v3/p15
  • This publication is cited in the following 12 articles:
    1. V. V. Prokofev, A. V. Zabrodin, “Elliptic solutions of the Toda lattice hierarchy and the elliptic Ruijsenaars–Schneider model”, Theoret. and Math. Phys., 208:2 (2021), 1093–1115  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Prokofev V., Zabrodin A., “Elliptic Solutions to Matrix Kp Hierarchy and Spin Generalization of Elliptic Calogero-Moser Model”, J. Math. Phys., 62:6 (2021), 061502  crossref  mathscinet  isi
    3. Prokofev V., Zabrodin A., “Elliptic Solutions to the Kp Hierarchy and Elliptic Calogero-Moser Model”, J. Phys. A-Math. Theor., 54:30 (2021), 305202  crossref  mathscinet  isi
    4. V. V. Prokofev, A. V. Zabrodin, “Matrix Kadomtsev–Petviashvili Hierarchy and Spin Generalization of Trigonometric Calogero–Moser Hierarchy”, Proc. Steklov Inst. Math., 309 (2020), 225–239  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Zabrodin A., “Kp Hierarchy and Trigonometric Calogero-Moser Hierarchy”, J. Math. Phys., 61:4 (2020)  crossref  mathscinet  isi  scopus
    6. Prokofev V., Zabrodin A., “Toda Lattice Hierarchy and Trigonometric Ruijsenaars?Schneider Hierarchy”, J. Phys. A-Math. Theor., 52:49 (2019), 495202  crossref  mathscinet  isi  scopus
    7. Alex Kasman, “Bispectrality of NN-Component KP Wave Functions: A Study in Non-Commutativity”, SIGMA, 11 (2015), 087, 22 pp.  mathnet  crossref
    8. Haine L., Horozov E., Iliev P., “The trigonometric Grassmannian and a difference WW-algebra”, Transform. Groups, 15:1 (2010), 92–114  crossref  mathscinet  zmath  isi  elib  scopus
    9. Fehér L., Klimčík C., “On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models”, J. Phys. A, 42:18 (2009), 185202, 13 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Bergvelt M., Gekhtman M., Kasman A., “Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy”, Math. Phys. Anal. Geom., 12:2 (2009), 181–200  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Haine L., Horozov E., Iliev P., “Trigonometric Darboux transformations and Calogero–Moser matrices”, Glasg. Math. J., 51:A (2009), 95–106  crossref  mathscinet  zmath  isi  scopus
    12. Mukhin E., Tarasov V., Varchenko A., “Bispectral and (glN,glM) dualities, discrete versus differential”, Adv. Math., 218:1 (2008), 216–265  crossref  mathscinet  zmath  isi  elib  scopus
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    Symmetry, Integrability and Geometry: Methods and Applications
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