厄米对称空间上的非线性Schrodinger方程的量子反散射方法Ⅱ:D.Ⅲ.情形

QUANTUM INVERSE SCATTERING METHOD FOR NONLINEAR SCHRODINGER EQUATIONS ON HERMITEAN SYMMETRIC SPACESⅡ:D.Ⅲ.CASE

本文在反散射方法的框架内详细研究了厄米对称空间D.■上的非线性Schrdinger方程。给出了经典r 矩阵和量子R 矩阵的明显形式,从而建立了散射数数据之间的经典Poisson 括号和量子对易关系。

A nonlinear Schr(?)dinger equation on the Hermitean symmetric space D.Ⅲ.is studied in detail inthe framework of the quantum inverse scattering method.The classical r matrix and the quantum Rmatrix are explicitly presented,thus establishing the classical poisson brackets and the quantum commu-tation relations among the scattering data operators.