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A note on critical points of integrals of soliton equations

A note on critical points of integrals of soliton equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

A note on critical points of integrals of soliton equations

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-010-0002-x
Publisher site
See Article on Publisher Site

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.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 21, 2010

References