Elliptic Families of Solutions of the Kadomtsev-Petviashvili Equation and the Field Elliptic Calogero-Moser System

Abstract

We present the Lax pair for the field elliptic Calogero-Moser system and establish a connection between this system and the Kadomtsev-Petviashvili equation. Namely, we consider elliptic families of solutions of the KP equation, such that their poles satisfy a constraint of being balanced. We show that the dynamics of these poles is described by a reduction of the field elliptic CM system. We construct a wide class of solutions to the field elliptic CM system by showing that any N-fold branched cover of an elliptic curve gives rise to an elliptic family of solutions of the KP equation with balanced poles.

arXiv comment16 pages

References in corpus (2)

• Quantum Integrable Systems and Elliptic Solutions of Classical Discrete Nonlinear Equations
• Elliptic Calogero-Moser system from two dimensional current algebra

Cited by in corpus (3)

• Field analogue of the Ruijsenaars-Schneider model
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Elliptic families of solutions to constrained Toda hierarchy