On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system
C. Bartocci, G. Falqui, I. Mencattini, G. Ortenzi, M. Pedroni
TL;DR
This paper reveals the geometric origin of the bi-Hamiltonian structure in the rational Calogero-Moser system, connecting it to a simple Poisson pair on the cotangent bundle of gl(n,R) and discussing its relation to the Lax formalism.
Contribution
It introduces a geometric perspective by deriving the bi-Hamiltonian structure via a double projection from a basic Poisson pair, linking it to the Lax formalism.
Findings
Bi-Hamiltonian structure obtained from a simple Poisson pair
Connection established with the Lax formalism
Provides geometric insight into the Calogero-Moser system
Abstract
We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Nonlinear Waves and Solitons