ANZIAM J.
44 (2002), 129139

Binary constrained flows and separation of variables for soliton equations

WenXiu Ma
Department of Mathematics
University of South Florida, Tampa
FL 336205700
USA
mawx@math.usf.edu



Yunbo Zeng
Department of Mathematical Sciences
Tsinghua University
Beijing 100084
China
yzeng@tsinghua.edu.cn



Abstract

In contrast to monoconstrained flows with
N
degrees of freedom, binary constrained flows of
soliton equations, admitting 2 x 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.

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