非局部AB-NLS方程的双线性Bäcklund和Darboux变换与非线性波

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 370-381.

非局部AB-NLS方程的双线性Bäcklund和Darboux变换与非线性波

申亚丽¹(),姚若侠^2,*(),夏亚荣³()

¹ 运城学院数学与信息技术学院山西运城 044000
² 陕西师范大学计算机科学学院西安 710119
³ 西安文理学院信息与工程学院西安 710065

收稿日期:2020-03-09 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 姚若侠 E-mail:shenyali422@163.com;rxyao2@hotmail.com;xiayarong2014@126.com
作者简介:申亚丽, E-mail: shenyali422@163.com|夏亚荣, E-mail: xiayarong2014@126.com
基金资助:
国家自然科学基金(11471004);国家自然科学基金(12001424);国家自然科学基金(11775047);山西省高等院校科技创新项目(2019L0868);陕西省自然科学基金(2018JQ-1045);运城学院博士科研启动项目(YQ-2020019)

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

Yali Shen¹(),Ruoxia Yao^2,*(),Yarong Xia³()

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)

摘要/Abstract

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-Schrödinger（AB-NLS）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Bäcklund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.

关键词: AB-NLS系统, 双线性Bäcklund变换, Darboux变换, 非线性波

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

中图分类号:

O175

申亚丽,姚若侠,夏亚荣. 非局部AB-NLS方程的双线性Bäcklund和Darboux变换与非线性波[J]. 数学物理学报, 2021, 41(2): 370-381.

Yali Shen,Ruoxia Yao,Yarong Xia. On a Nonlocal Alice-Bob-Schrödinger Equation: Bilinear Bäcklund and Darboux Transformations and Nonlinear Waves[J]. Acta mathematica scientia,Series A, 2021, 41(2): 370-381.

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