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Binary constrained flows and separation of variables for soliton equations

Published online by Cambridge University Press:  17 February 2009

Wen-Xiu Ma  and
Yunbo Zeng
Wen-Xiu Ma
Affiliation:
Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA; e-mail: mawx@math.usf.edu.
Yunbo Zeng
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; e-mail: yzeng@tsinghua.edu.cn.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 129 - 139
Copyright
Copyright © Australian Mathematical Society 2002

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