Elliptic families of solutions of the Kadomtsev-Petviashvili equation, and the field analogue of the elliptic Calogero-Moser system
As was shown in \textit{H. Airault, H. McKean} and \textit{J. Moser} [Commun. Pure Appl. Math. 30, 95--148 (1977; Zbl 0338.35024], the dynamics of poles of rational solutions of the Korteweg-de Vries (KdV) equation can be described in terms of the Calogero-Moser (CM) system. In the paper under review, this result is generalized to the case of elliptic families of solutions to the Kadomtsev-Petviashvili (KP) equation. Namely, the authors prove that the dynamics of the so-called balanced poles of such families is described by a reduction of the field analog of the elliptic CM system. It is also shown that any \(N\)-fold branched cover of an elliptic curve gives rise to an elliptic family of solutions to the KP equation with balanced poles thus providing a wide class of solutions to the field elliptic CM system.
scientific article; zbMATH DE number 1930673