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 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.
- Publication:
-
Analysis and Mathematical Physics
- Pub Date:
- March 2011
- DOI:
- 10.1007/s13324-010-0002-x
- arXiv:
- arXiv:1005.3741
- Bibcode:
- 2011AnMP....1...15K
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 20 pages