Elliptic families of solutions of the Kadomtsev-Petviashvili equation, and the field analogue of the elliptic Calogero-Moser system
type: Item
instance of: scholarly article
title: Elliptic families of solutions of the Kadomtsev-Petviashvili equation, and the field analogue of the elliptic Calogero-Moser system
zbMATH Open document ID: 1033.37032
DOI: 10.1023/A:1021706525301
author: A. A. Akhmetshin
author: Igor Krichever
author: Yu. S. Vol'vovskij
publication date: 2004-03-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K20
Mathematics Subject Classification ID: 14H70
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1930673
zbMATH Keywords: Calogero-Moser system
zbMATH Keywords: Elliptic family
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: Lax pair
reviewed by: Igor Potemine
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1930673