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.
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Akhmetshin, A.A., Krichever, I.M. & Volvovski, Y.S. Elliptic Families of Solutions of the Kadomtsev--Petviashvili Equation and the Field Elliptic Calogero--Moser System. Functional Analysis and Its Applications 36, 253–266 (2002). https://doi.org/10.1023/A:1021706525301
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DOI: https://doi.org/10.1023/A:1021706525301