New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
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DOI：
10.1143/jpsj.64.1085
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发表时间：
1995-04
影响因子：
1.7
通讯作者：
W. Ma
中科院分区：
文献类型：
--
作者：
W. Ma
通过引入Bargmann对称约束，将KdV可积族的谱问题和伴随谱问题转化为有限维Liouville意义下的可积Hamilton系统.同时，在该系统（即空间部分）的控制下，约束Lax对和伴随Lax对的时间部分被约化为一族新的Liouville意义下的可交换的有限维可积Hamilton系统，其Hamilton函数构成约束Lax对和伴随Lax对空间部分的一系列运动积分.
Through taking a Bargmann symmetry constraint, the spectral problem and the adjoint spectral problem of KdV integrable hierarchy are transformed into a finite dimensional integrable Hamiltonian system in the Liouville sense. Meantime, under the control of this system (i.e. the spatial part), the time parts of the constrained Lax pairs and adjoint Lax pairs are reduced to a new hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, whose Hamiltonian functions constitute a series of integrals of motion for the spatial part of the constrained Lax pairs and adjoint Lax pairs.