Binary constrained flows and separation of variables for soliton equations

Abstract

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2 × 2 Lax matrices, have 2N degrees of freedom. Currently existing methods only enable Lax matrices to yield the first N pairs of canonical separated variables. An approach for constructing the second N pairs of canonical separated variables with N additional separated equations is introduced. The Jacobi inversion problems for binary constrained flows are then established. Finally, the separability of binary constrained flows together with the factorization of soliton equations by the spatial and temporal binary constrained flows leads to the Jacobi inversion problems for soliton equations. © Australian Mathematical Society 2002.