Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-15
Physics
High Energy Physics
High Energy Physics - Theory
35 pages, LaTex. Macros file elsart.sty is used (it was submitted by the authors to solv-int@xyz.lanl.gov library macroses),e-
Scientific paper
10.1016/0167-2789(95)00139-U
Flows on the moduli space of the algebraic Riemann surfaces, preserving the periods of the corresponding solutions of the soliton equations are studied. We show that these flows are gradient with respect to some indefinite symmetric flat metric arising in the Hamiltonian theory of the Whitham equations. The functions generating these flows are conserved quantities for all the equations simultaneously. We show that for 1+1 systems these flows can be imbedded in a larger system of ordinary nonlinear differential equations with a rational right-hand side. Finally these flows are used to give a complete description of the moduli space of algebraic Riemann surfaces corresponding to periodic solutions of the nonlinear Schr\"odinger equation.
Grinevich Petr G.
Schmidt Martin Ulrich
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