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

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

2002-03-21

arxiv.org/abs/hep-th/0203192v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages

Scientific paper

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.

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