具有吸引作用的量子非线性Schrdinger模型的反散射变换(英文)

INVERSE SCATTERING TRANSFORM FOR THE QUANTUM NONLINEAR SCHR?DINGER MODEL WITH ATTRACTIVE INTERACTION

本文构造出具有吸引作用的量子非线性Schr dinger模型完备的Gelfane Levitan方程组。我们避免了在方程中引进过去文献中所用的依赖坐标参量的算子或病态定义的算子 .从而所得的非线性Schr dinger模型的Heisenberg场算子完全由良好定义的散射数据算子确定 .

The system of the Gelfand Levitan equations for the quantum nonlinear Schrdinger model with attractive interaction is obtained,in which we have avoided introducing ill defined operators or operators depending on coordinate parameter as those in early works.The Heisenberg field operator of the nonlinear Schrdinger model is completely determined by the well defined scattering data operators.