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Functional Analysis and Its Applications

, Volume 36, Issue 4, pp 253–266 | Cite as

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

  • A. A. Akhmetshin
  • I. M. Krichever
  • Yu. S. Volvovski
Article

Abstract

We present a 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.

KP equation, Calogero--Moser system, Lax pair 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. A. Akhmetshin
  • I. M. Krichever
  • Yu. S. Volvovski

There are no affiliations available

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