Binary constrained flows and separation of variables for soliton equations
Binary constrained flows and separation of variables for soliton equations
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DOI：
10.1017/s1446181100007987
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发表时间：
2001-04
期刊：
影响因子：
--
通讯作者：
W. Ma;Yunbo Zeng
中科院分区：
文献类型：
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作者：
W. Ma;Yunbo Zeng
与具有N个自由度的单约束流相比，具有2×2 Lax矩阵的孤子方程的二元约束流具有2N个自由度。目前，现有的方法仅使Lax矩阵能够产生前N对规范分离变量。介绍了一种利用N个附加分离方程构造第二个N对规范分离变量的方法。然后建立了双约束流的Jacobi逆问题。最后，双约束流的可分性以及空间和时间双约束流对孤子方程的分解导致了孤子方程的Jacobi逆问题。
Abstract 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.