scholarly journals Nonlocal nonlinear Schrödinger equation and its discrete version: Soliton solutions and gauge equivalence

2016 ◽  
Vol 57 (8) ◽  
pp. 083507 ◽  
Author(s):  
Li-Yuan Ma ◽  
Zuo-Nong Zhu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Discrete Version ◽  
Nonlinear Schrödinger ◽  
Gauge Equivalence ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

scholarly journals The Soliton Solutions and Long-Time Asymptotic Analysis for an Integrable Variable Coefficient Nonlocal Nonlinear Schrödinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Guiying Chen ◽  
Xiangpeng Xin ◽  
Feng Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

An integrable variable coefficient nonlocal nonlinear Schrödinger equation (NNLS) is studied; by employing the Hirota’s bilinear method, the bilinear form is obtained, and the N -soliton solutions are constructed. In addition, some singular solutions and period solutions of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the two-soliton solution is analyzed to prove that the collision of the two-soliton is elastic.

scholarly journals On Solutions of an Extended Nonlocal Nonlinear Schrödinger Equation in Plasmas

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1099
Author(s):  
Yehui Huang ◽  
Hongqing Jing ◽  
Min Li ◽  
Zhenjun Ye ◽  
Yuqin Yao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

The parity-time symmetric nonlocal nonlinear Schrödinger equation with self-consistent sources (PTNNLSESCS) is used to describe the interaction between an high-frequency electrostatic wave and an ion-acoustic wave in plasmas. In this paper, the soliton solutions, rational soliton solutions and rogue wave solutions are derived for the PTNNLSESCS via the generalized Darboux transformation. We find that the soliton solutions can exhibit the elastic interactions of different type of solutions such as antidark-antidark, dark-antidark, and dark-dark soliton pairs on a continuous wave background. Also, we discuss the degenerate case in which only one antidark or dark soliton remains. The rogue wave solution is derived in some specially chosen situations.

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