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Analysis and Mathematical Physics

, Volume 1, Issue 1, pp 15–35 | Cite as

A note on critical points of integrals of soliton equations

  • I. M. Krichever
  • D. V. Zakharov
Article

Abstract

We consider the problem of extending the integrals of motion of soliton equations to the space of all finite-gap solutions. We consider the critical points of these integrals on the moduli space of Riemann surfaces with marked points and jets of local coordinates. We show that the solutions of the corresponding variational problem have an explicit description in terms of real-normalized differentials on the spectral curve. Such conditions have previously appeared in a number of problems of mathematical physics.

Keywords

Modulus Space Riemann Surface Meromorphic Function Elliptic Curve Marked Point 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia
  3. 3.Kharkevich Institute for Information Transmission ProblemsMoscowRussia

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