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

Abstract

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

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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References 30

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

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