On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
B.G. Pusztai
TL;DR
This paper develops a quadratic r-matrix framework and provides a Lax representation for the rational BC(n) Ruijsenaars-Schneider-van Diejen system, enhancing understanding of its integrable structure.
Contribution
It introduces a quadratic r-matrix structure for the system with three coupling parameters and offers a Lax representation, advancing the mathematical understanding of this integrable model.
Findings
Constructed a quadratic r-matrix structure for the system.
Provided a Lax representation of the dynamics.
Extended the integrability framework for the BC(n) Ruijsenaars-Schneider-van Diejen system.
Abstract
In this paper, we construct a quadratic r-matrix structure for the classical rational BC(n) Ruijsenaars-Schneider-van Diejen system with the maximal number of three independent coupling parameters. As a byproduct, we provide a Lax representation of the dynamics as well.
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