A note on critical points of integrals of soliton equations
Algebraic Geometry
2010-05-21 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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
Cite
@article{arxiv.1005.3741,
title = {A note on critical points of integrals of soliton equations},
author = {Igor Krichever and Dmitry Zakharov},
journal= {arXiv preprint arXiv:1005.3741},
year = {2010}
}
Comments
20 pages