English

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