A note on critical points of integrals of soliton equations
Abstract
We consider the problem of extending the integrals of motion of soliton equations to the space of all finitegap 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 realnormalized differentials on the spectral curve. Such conditions have previously appeared in a number of problems of mathematical physics.
 Publication:

Analysis and Mathematical Physics
 Pub Date:
 March 2011
 DOI:
 10.1007/s133240100002x
 arXiv:
 arXiv:1005.3741
 Bibcode:
 2011AnMP....1...15K
 Keywords:

 Modulus Space;
 Riemann Surface;
 Meromorphic Function;
 Elliptic Curve;
 Marked Point;
 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 20 pages