  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.
