Abstract
Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bogdanov, L. V. and Konopelchenko, B. G. (1999) Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser System, solv-int/9912005.
Bogdanov, L. V. and Konopelchenko, B. G. (1998) Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy., J. Math. Phys. 39(9), 4683–4700.
Bogdanov, L. V. and Konopelchenko, B. G. (1998) Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies., J. Math. Phys. 39(9), 4701–4728.
Bogdanov, L. V. (1999) Analytic-Bilinear Approach to Integrable Hierarchies, Kluwer Academic Publishers, Dordrecht.
Date, E., Kashiwara, M., Jimbo, M., Miwa, T. (1983) Transformation groups for soliton equations, in M. Jimbo and T. Miwa (eds.), Nonlinear integrable systems—classical theory and quantum theory (Kyoto, 1981), World Scientific Publishing, Singapore, pp. 39–119.
Novikov, S. P., Manakov, S. V., Pitaevskiĭ, L. P., Zakharov, V. E. (1984) Theory of solitons. The inverse scattering method, Consultants Bureau [Plenum], New York-London.
Orlov, A. Yu. and Shuhnan, E.I. (1986) Additional symmetries for integrable equations and conformai algebra representation, Lett. Math. Phys. 12, 171–179.
Grinevich, P.G. and Orlov, A. Yu. (1990) Krichever-Novikov problem..., Funct. Analys. Appl. 24, 72–74.
Orlov, A. Yu. (1993) Volterra Operator Algebra for Zero Curvature Representation. Universality of KP, in A. Fokas et al (eds.), Nonlinear Processes in Physics. Potsdam-Kiev, 1991, Springer, Berlin, pp. 126–131. Orlov, A. Yu. (1994), Ph. D. Thesis, Chernogolovka.
Konopelchenko, B. and Strampp. W. (1991) The AKNS hierarchy as symmetry constraint of the KP hierarchy, Inverse Problems 7(5), L17–L24.
Konopelchenko, B. and Strampp, W. (1992) New reductions of the Kadomtsev-Petviashvili and twodimensional Toda lattice hierarchies via symmetry constraints, J. Math. Phys. 33(11), 3676–3686.
Krichever, I.M. (1978) On rational solutions of Kadomtsev-Petviashvili equation and integrable systems of N particles on the line, Funct. Anal, i Pril. 12(1), 76–78.
Shiota, T. (1994) Calogero-Moser hierarchy and KP hierarchy, J. Math. Phys. 35, 5844–5849.
Ueno K. and Takasaki K. (1984) Toda lattice hierarchy in K. Okamoto (ed.) Group representations and systems of differential equations (Tokyo 1982) North-Holland Amsterdam-New York pp. 1–95
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bogdanov, L.V., Konopelchenko, B.G., Orlov, A.Y. (2001). Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy. In: Aratyn, H., Sorin, A.S. (eds) Integrable Hierarchies and Modern Physical Theories. NATO Science Series, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0720-7_9
Download citation
DOI: https://doi.org/10.1007/978-94-010-0720-7_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6963-9
Online ISBN: 978-94-010-0720-7
eBook Packages: Springer Book Archive