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 TMF, 2001, Volume 128, Number 2, Pages 205–225 (Mi tmf492)

Construction of Separation Variables for Finite-Dimensional Integrable Systems

A. V. Tsiganov

St. Petersburg State University, Faculty of Physics

Abstract: We consider a class of integrable systems such that solutions of the corresponding Hamilton–Jacobi equation depend on $n+m$ arbitrary parameters and are represented as products of flat curves. The first n parameters are identified with the values of the integrals of motion. The remaining parameters enter the definition of the integrals of motion as arbitrary constants (charges) and can be used to find separation variables. We show that on the coadjoint orbits of Lie groups, the Casimir operators not only generate a family of integrals but also allow constructing separation variables.

DOI: https://doi.org/10.4213/tmf492

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English version:
Theoretical and Mathematical Physics, 2001, 128:2, 1007–1024

Bibliographic databases:

Citation: A. V. Tsiganov, “Construction of Separation Variables for Finite-Dimensional Integrable Systems”, TMF, 128:2 (2001), 205–225; Theoret. and Math. Phys., 128:2 (2001), 1007–1024

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf492
• https://doi.org/10.4213/tmf492
• http://mi.mathnet.ru/eng/tmf/v128/i2/p205

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This publication is cited in the following articles:
1. Sergyeyev, A, “Generalized Stackel transform and reciprocal transformations for finite-dimensional integrable systems”, Journal of Physics A-Mathematical and Theoretical, 41:10 (2008), 105205
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