利用李代数构造非线性可积及双可积哈密顿耦合

Lie Algebras for Constructing Nonlinear Integrable and Bi-Integrable Hamiltonian Couplings

中文关键词:  李代数  可积耦合  双可积耦合  哈密顿结构

英文关键词:Lie algebra  integrable couplings  bi-integrable couplings  Hamiltonian structure

中文摘要:

      首先从一个常用李代数的线性组合出发,给出两种用于构造非线性可积耦合和双可积耦合的李代数.接着引入了一个可积的哈密顿系统,通过约化,从中得到了一些演化方程.最后利用给出的两种李代数及变分恒等式推导出这个可积哈密顿系统的非线性可积和双可积哈密顿耦合.本文给出的方法也适用于构造其他可积系统的非线性可积和双可积哈密顿耦合.

英文摘要:

      With the help of a Lie algebra, two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings. For illustrating the application of the Lie algebras, an integrable Hamiltonian system is obtained, from which some reduced evolution equations are presented. Finally, Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity. The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.