A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system
A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system
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DOI：
10.1016/j.chaos.2005.09.016
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发表时间：
2006-05
影响因子：
7.8
通讯作者：
T. Xia;Fucai You
中科院分区：
文献类型：
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作者：
T. Xia;Fucai You
构造了高维loop代数A2的一个子代数，由此设计了一个新的3×3等谱问题.利用屠维岳的格式，得到了Liouville意义下的可积Hamilton方程族，它具有三Hamilton结构。作为本文所提出的族的约化情形，得到了广义MKdV方程。通过建立二元对称约束，给出了该族的三个约束流，并将其化为Hamilton系统。最后，通过构造一个高维loop代数得到一个可积耦合系统。
A subalgebra of higher-dimension loop algebra A2˜ is constructed, from which a new 3×3 isospectral problem is designed. By making use of Tu’s scheme, an integrable Hamiltonian hierarchy of equations in the sense of Liouville is obtained, which possesses tri-Hamiltonian structure. As reduction cases of the hierarchy presented in this paper, the generalized MKdV equation is engendered. By establishing binary symmetric constraints, three constrained flows of the hierarchy are presented, which are then reduced to Hamiltonian systems. Finally, an integrable coupling system is obtained by constructing a high-dimension loop algebra.