【摘要】 非局部Alice-Bob系统可用来描述自然科学和社会科学中不同空间或时间的若干事件,这些事件在本质上是相互联系或者相互纠缠的.该文研究一个非局部Alice-Bob-Schr?dinger(ABNLS)系统,它由著名的AKNS系统约化所得,是一个真正的可积两地系统.首先通过双线性方法获得该系统的双线性B?cklund变换,进而构建该系统的n阶Darboux变换(DT).在此基础上,给出了非局部AB-NLS方程不同于NLS方程的非线性波,并分析了解的奇异性.更多还原

【Abstract】 Many events entangled or connected inherently however not recognized by human may happy at different spaces or different times in natural and social sciences can be described by using nonlocal Alice and Bob systems.In this paper,a newly proposed nonlinear Schrodinger equation(AB-NLS) derived from the well-known AKNS system is investigated,which is a real integrable two-place system.We obtain not only a bilinear Backlund transformation for the unreduced AB-NLS by the bilinear method,but also an n-fold Darboux transformation for the reduced AB-NLS.Armed with them we present some nonlinear waves for the nonlocal AB-NLS,which are quite different from that of the NLS equation and the solutions are analyzed about the singularity.更多还原