Discrete-time Calogero-Moser system and Lagrangian 1-form structure
by Professor Frank W Nijhoff
Abstract: The discrete-time Calogero-Moser (CM) system, i.e. a system of ordinary difference equations which reduces to the equations of motion of the rational CM many-body system, arises as a reduction of a semi-discrete version of the KP equation. We discuss the Lagrange structure for this model as well as of its continuum limit giving rise to a description in terms of 'Lagrangian 1-forms" which allows us to capture the hierarchy of higher-order CM equations in one framework. We will argue in this context that the existence of such a Lagrange 1-form structure implies integrability. If time allows a generalization to the rational Ruijsenaars model is given.