Riemann–Hilbert approach and soliton classification for a nonlocal integrable nonlinear Schrödinger equation of reverse-time type

2021 ◽  
Author(s):  
Jianping Wu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Reverse Time ◽  
Nonlinear Schrödinger ◽  
Time Type

Soliton solutions to the nonlocal non-isospectral nonlinear Schrödinger equation

2020 ◽  
Vol 34 (25) ◽  
pp. 2050219 ◽  
Author(s):  
Wei Feng ◽  
Song-Lin Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Reverse Time ◽  
Nonlinear Schrödinger ◽  
Reduced Equations ◽  
Double Wronskian ◽  
The One

In this paper we study the nonlocal reductions for the non-isospectral Ablowitz-Kaup-Newell-Segur equation. By imposing the real and complex nonlocal reductions on the non-isospectral Ablowitz-Kaup-Newell-Segur equation, we derive two types of nonlocal non-isospectral nonlinear Schrödinger equations, in which one is real nonlocal non-isospectral nonlinear Schrödinger equation and the other is complex nonlocal non-isospectral nonlinear Schrödinger equation. Of both of these two equations, there are the reverse time nonlocal type and the reverse space nonlocal type. Soliton solutions in terms of double Wronskian to the reduced equations are obtained by imposing constraint conditions on the double Wronskian solutions of the non-isospectral Ablowitz-Kaup-Newell-Segur equation. Dynamics of the one-soliton solutions are analyzed and illustrated by asymptotic analysis.

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