双光子余代数对称性的N维可积性
N-dimensional integrability from two-photon coalgebra symmetry
摘要：
利用双光子Lie-Poisson余代数构造了一类具有N个自由度的Hamilton系统，它们至少具有（N-2）个函数独立的对合运动积分.的一组（N-2）常数的运动被证明是一个普遍的所有这些哈密顿量，无关的依赖，后者对几个任意函数和N个自由参数。在这一大类拟可积N维哈密顿量中，通过分析双光子代数的子余代数结构，明确地找到了一个新的独立积分，从而确定了新的完全可积系统族.特别是，新的完全可积的N维哈密顿描述自然系统，测地线流和静态电磁哈密顿。
英文摘要：
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of (N-2) constants of the motion is shown to be a universal one for all these Hamiltonians, irrespectively of the dependence of the latter on several arbitrary functions and N free parameters. Within this large class of quasi-integrable N-dimensional Hamiltonians, new families of completely integrable systems are identified by finding explicitly a new independent integral through the analysis of the sub-coalgebra structure of the two-photon algebra. In particular, new completely integrable N-dimensional Hamiltonians describing natural systems, geodesic flows and static electromagnetic Hamiltonians are presented.
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