Separation of variables for soliton equations via their binary constrained flows

Details Separation of variables for soliton equations via their binary constrained flows Separation of variables for soliton equations via their binary constrained flows

1999-11-17

arxiv.org/abs/solv-int/9911007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

39 pages, Amstex

Scientific paper

10.1063/1.533105

Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs of canonical separated variables can be introduced via their Lax matrices by using the normal method. A new method to introduce the other N pairs of canonical separated variables and additional separated equations is proposed. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies.

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