Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 370-381.

Previous Articles     Next Articles

On a Nonlocal Alice-Bob-Schrödinger Equation: Bilinear Bäcklund and Darboux Transformations and Nonlinear Waves

Yali Shen1(),Ruoxia Yao2,*(),Yarong Xia3()   

  1. 1 School of Mathematics and Information Technology, Yuncheng University, Shanxi Yuncheng 044000
    2 School of Computer Science, Shaanxi Normal University, Xi'an 710119
    3 School of Information and Engineering, Xi'an University, Xi'an 710065
  • Received:2020-03-09 Online:2021-04-26 Published:2021-04-29
  • Contact: Ruoxia Yao E-mail:shenyali422@163.com;rxyao2@hotmail.com;xiayarong2014@126.com
  • Supported by:
    the NSFC(11471004);the NSFC(12001424);the NSFC(11775047);the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2019L0868);the NSF of Shaanxi Province(2018JQ-1045);the Doctoral Research Project of Yuncheng University(YQ-2020019)

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 Schrödinger 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 Bäcklund 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.

Key words: AB-NLS system, Bilinear Bäcklund transformation, Darboux transformation, Nonlinear waves

CLC Number: 

  • O175
Trendmd