ANZIAM  J.  44 (2002), 129-139
Binary constrained flows and separation of variables for soliton equations

Wen-Xiu Ma
  Department of Mathematics
  University of South Florida, Tampa
  FL 33620-5700
Yunbo Zeng
  Department of Mathematical Sciences
  Tsinghua University
  Beijing 100084

In contrast to mono-constrained 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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