A new method to introduce additional separated variables for high-order binary constrained flows

Details A new method to introduce additional separated variables for high-order binary constrained flows A new method to introduce additional separated variables for high-order binary constrained flows

2000-01-10

arxiv.org/abs/nlin/0001010v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

34 pages, AmsTex, to be published in J. Phys. A

Scientific paper

10.1088/0305-4470/33/3/314

Degrees of freedom for high-order binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that $N+k_0$ pairs of canonical separated variables for their separation of variables can be introduced directly via their Lax matrices. In present paper we propose a new method to introduce the additional $N$ pairs of canonical separated variables and $N$ additional separated equations. The Jacobi inversion problems for high-order binary constrained flows and for soliton equations are also established. This new method can be applied to all high-order binary constrained flows admitting $2\times 2$ Lax matrices.

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