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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2002
- DOI:
- 10.48550/arXiv.hep-th/0203192
- arXiv:
- arXiv:hep-th/0203192
- Bibcode:
- 2002hep.th....3192A
- Keywords:
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- High Energy Physics - Theory;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 16 pages