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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 4, Pages 1–17
DOI: https://doi.org/10.4213/faa215 (Mi faa215) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Elliptic Families of Solutions of the Kadomtsev–Petviashvili Equation and the Field Elliptic Calogero–Moser System

A. A. Akhmetshina, Yu. S. Vol'vovskiia, I. M. Kricheverbc

a Columbia University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (216 kB) Citations (20)
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DOI: https://doi.org/10.4213/faa215
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.
Keywords: KP equation, Calogero–Moser system, Lax pair.
Received: 13.05.2002
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 4, Pages 253–266
DOI: https://doi.org/10.1023/A:1021706525301
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Elliptic Families of Solutions of the Kadomtsev–Petviashvili Equation and the Field Elliptic Calogero–Moser System”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 1–17; Funct. Anal. Appl., 36:4 (2002), 253–266
Citation in format AMSBIB
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\paper Elliptic Families of Solutions of the Kadomtsev--Petviashvili Equation and the Field Elliptic Calogero--Moser System
\jour Funktsional. Anal. i Prilozhen.
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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