摘要
通过对广义非线性Schrodinger方程的Backlund变换加上周期固定点条件,得到了一组有限维系统,并用r-矩阵方法证明了它们的完全可积性和Hamilton形式。同时还指出存在一个R-矩阵使得这些系统的量子化形式的可积性可由量子反散射方法证明。在这些量子可积系统中,包含了一种非齐性的ⅩⅩⅩ模型作为特例。
By imposing the periodic fixed point condition to the Backlund transformations(BTs) of the generalized nonlinear Schrodinger equation, a class of finite dimensional sysems are obtained. Their Hamiltonian structures and the integrability can be proved by using the r—matrix method. An R—matrix also exists such that the quantum analogue of these systems fit in with the scheme of the quantum inverse scattering method. A particular example of our quantum system is a kind of the inhomogeneous ⅩⅩⅩ model.
