scholarly journals Darboux transformation and analytic solutions of the discrete PT-symmetric nonlocal nonlinear Schrödinger equation

2017 ◽  
Vol 63 ◽  
pp. 88-94 ◽  
Author(s):  
Tao Xu ◽  
Hengji Li ◽  
Hongjun Zhang ◽  
Min Li ◽  
Sha Lan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

scholarly journals Rational Solutions of a Weakly Coupled Nonlocal Nonlinear Schrödinger Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Huijuan Zhou ◽  
Chuanzhong Li ◽  
Yueh-Lung Lin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Nonlinear Schrödinger ◽  
Weakly Coupled ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

In this article, we investigate an integrable weakly coupled nonlocal nonlinear Schrödinger (WCNNLS) equation including its Lax pair. Afterwards, Darboux transformation (DT) of the weakly coupled nonlocal NLS equation is constructed, and then the degenerated Darboux transformation can be got from Darboux transformation. Applying the degenerated Darboux transformation, the new solutions (q[1],r[1]) and self-potential function(V[1])are created from the known solutions (q,r). The (q[1],r[1]) satisfy the parity-time (PT) symmetry condition, and they are rational solutions with two free phase parameters of the weakly coupled nonlocal nonlinear Schrödinger equation. From the plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution are produced.

Rational soliton solutions of the nonlocal nonlinear Schrödinger equation by the KP reduction method

2019 ◽  
Vol 33 (30) ◽  
pp. 1950362
Author(s):  
Donghua Wang ◽  
Yehui Huang ◽  
Xuelin Yong ◽  
Jinping Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Reduction Method ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

In this paper, we present the construction of the rational solutions to the nonlocal nonlinear Schrödinger equation by the bilinear method and KP reduction method. The solutions are given in determinant form, the first- and second-order rational solutions are analyzed for their dynamic behaviors.

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