2016/01/19 by Umpon Jairuk, Sikarin Yoo-Kong, Monsit Tanasittikosol · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/s0034-4877(17)30046-0
25 pages, 5 figures
arxiv created 2016/01/19 · arxiv updated 2017/08/23
In this work, we present another example of the Lagrangian 1-form structure for the hy- perbolic Calogero-Moser system both in discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole-reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. The key relation called the discrete-time closure relation is directly obtained from the compatibility between the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained through two successive continuum limits. The continuous-time closure relation, which is a consequence of continuum limits on the discrete-time one, is also shown to hold.