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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 4, Pages 1–17 (Mi faa215)  

This article is cited in 10 scientific papers (total in 10 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

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


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English version:
Functional Analysis and Its Applications, 2002, 36:4, 253–266

Bibliographic databases:

UDC: 517.9
Received: 13.05.2002

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
\by A.~A.~Akhmetshin, Yu.~S.~Vol'vovskii, I.~M.~Krichever
\paper Elliptic Families of Solutions of the Kadomtsev--Petviashvili Equation and the Field Elliptic Calogero--Moser System
\jour Funktsional. Anal. i Prilozhen.
\yr 2002
\vol 36
\issue 4
\pages 1--17
\jour Funct. Anal. Appl.
\yr 2002
\vol 36
\issue 4
\pages 253--266

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    This publication is cited in the following articles:
    1. Fledrich, P, “Hyperelliptic osculating covers and KdV solutions periodic in tau”, International Mathematics Research Notices, 2006, 73476  mathscinet  zmath  isi  elib
    2. Gesztesy, F, “An explicit characterization of Calogero–Moser systems”, Transactions of the American Mathematical Society, 358:2 (2006), 603  crossref  mathscinet  zmath  isi  scopus
    3. I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Russian Math. Surveys, 63:6 (2008), 1011–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Ben-Zvi, D, “From solitons to many-body systems”, Pure and Applied Mathematics Quarterly, 4:2 (2008), 319  crossref  mathscinet  zmath  isi
    5. Nijhoff F., Atkinson J., “Elliptic N-soliton Solutions of ABS Lattice Equations”, Int Math Res Not, 2010, no. 20, 3837–3895  mathscinet  zmath  isi  elib
    6. Andrei V. Zotov, “$1+1$ Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp.  mathnet  crossref  mathscinet
    7. Ben-Zvi D., Nevins T., “D-bundles and integrable hierarchies”, J Eur Math Soc (JEMS), 13:6 (2011), 1505–1567  mathscinet  zmath  isi
    8. Treibich A., “Nonlinear evolution equations and hyperelliptic covers of elliptic curves”, Regular & Chaotic Dynamics, 16:3–4 (2011), 290–310  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Treibich A., “Hyperelliptic D-Osculating Covers and Rational Surfaces”, Bull. Soc. Math. Fr., 142:3 (2014), 379–409  crossref  mathscinet  zmath  isi  scopus
    10. A. Treibich, “Tangential Polynomials and Matrix KdV Elliptic Solitons”, Funct. Anal. Appl., 50:4 (2016), 308–318  mathnet  crossref  crossref  mathscinet  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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