The Jacobi Inversion Problem for Soliton Equations

Abstract

The separation of variables for x- and t_n-constrained flows of some kind of soliton hierarchy is shown. Since each equation in soliton hierarchy can be factorized into two commuting x- and t_n-constrained flow, the separability of x- and t_n-constrained flow provides the Jacobi inversion problem for soliton equations which is solvable in terms of Riemann theta function by standard Jacobi inversion technique. We use Kaup-Newell hierarchy to illustrate the method.