摘要
将和谱问题φ_(zz)+sum from i=1 to v u_iλ~iφ=αφ相联系的推广的Harry Dym方程族限制到它们递推算子的不变子空间,我们得到一族Hamilton系统。利用和谱问题有关的递推关系式,可以构造这族系统的守恒积分和Hamilton函数,从而证明,这些Hamilton系统在Liouville异义下是完全可积的且两两可交换的,同时它们的解满足推广的Harry Dym方程。
By restricting a hierarchy of generalized Harry Dym equations associated with the spectral problem φxx+sum from i=1 to N u_iχφ=αφ to the invariant subspace of their recursion operator, a hierarchy of Hamiltonian systems is obtained. The integrals of the motion and Hamiltonian functions for this hierarchy are constructed by using recursion formula related to the eigenvalue problem. The Hamiltonian systems are shown to be completely integrable in the sense of Liouville and to commute with each other. Also, their solution is shown to solve the generalized Harry Dym equation.
基金
Project supported by the Fund of the State Educational Committee of China.
关键词
HAMILTON系统
完全可积
守恒积分
completely integrable Hamiltonjan system, Harry Dym hierarchy, integral of the motion, eigenvalue problem, involution
