A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations
A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations
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DOI：
10.22436/jnsa.009.07.13
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Huanhe Dong;Tingting Chen;Long Chen;Yong Zhang
中科院分区：
文献类型：
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作者：
Huanhe Dong;Tingting Chen;Long Chen;Yong Zhang
提出了一个离散矩阵谱问题，推导出了离散可积系统的层次结构，该系统是Liouville可积的。并构造了层次结构的哈密顿结构。针对谱问题的二元非线性问题，给出了一族有限维完全可积系统和一个新的可积辛映射。特别是，在巴格曼约束条件下获得了两个显式公式。然后，根据种子对称性及其延拓性给出了离散可积系统的对称性。此外，离散晶格方程的解可以通过无穷小生成元的方式得到。 c ©2016 保留所有权利。
A discrete matrix spectral problem is proposed, the hierarchy of discrete integrable system is inferred, which are Liouville integrable. And the Hamiltonian structures of the hierarchy are constructed. A family of finite-dimensional completely integrable systems and a new integrable symplectic map are provided in terms of the binary nonlinearity of spectral problem. In particular, two explicit formulations are acquired under the condition of the bargmann constraints. After that, the symmetry of the discrete integrable systems is given on the basis of the seed symmetry and its prolongation. Moreover, the solution of the discrete lattice equation can be gained by the way of the infinitesimal generator. c ©2016 All rights reserved.