Abstract
It was shown in our previous paper that each equation in a soliton hierarchy can be factorized into two commuting x- and -finite-dimensional integrable Hamiltonian systems (FDIHSs). The separation variables for these FDIHSs are constructed by using their Lax representation. By means of the factorization and the separability of the FDIHSs we obtain the Jacobi inversion problem, which is solvable in terms of Riemann theta functions, for soliton equations. This provides a method analogous to the separation of variables for solving soliton equations.
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