Binary Constrained Flows and Separation of Variables for Soliton Equations

Details Binary Constrained Flows and Separation of Variables for Soliton Equations Binary Constrained Flows and Separation of Variables for Soliton Equations

2001-04-25

arxiv.org/abs/nlin/0104060v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, to appear in the proceedings of Kruskal 2000

Scientific paper

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2x2 Lax matrices, have 2N degrees of freedom. By means of the existing method, Lax matrices only yield the first N pairs of canonical separated variables. An approach for constructing the second N pairs of canonical separated variables with additional N 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.

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