2002/03/21 by A. Akhmetshin, Akhmetshin, A., I. Krichever +3 · 1 citation
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #nlin.SI
paper · pdf · doi:10.48550/arxiv.hep-th/0203192
16 pages
arxiv created 2002/03/21 · arxiv updated 2009/11/30
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.