Generalized Darboux transformation, semi-rational solutions and novel degenerate soliton solutions for a coupled nonlinear Schrödinger equation

2021 ◽  
Vol 136 (4) ◽  
Author(s):  
Hong-Yi Zhang ◽  
Yu-Feng Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Generalized Darboux Transformation

Exact solutions of the noncommutative and commutative nonlinear Schrödinger equation in 2 + 1 dimensions

2017 ◽  
Vol 32 (29) ◽  
pp. 1750158 ◽  
Author(s):  
H. Sarfraz ◽  
U. Saleem
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Localized Solutions ◽  
Multiple Soliton Solutions

In this paper, we presented a noncommutative (NC) generalization of nonlinear Schrödinger equation (NLSE) in 2 + 1 dimensions. A matrix Darboux transformation (MDT) is used to generate multiple soliton solutions for NC-NLSE and commutative NLSE in 2 + 1 dimensions. We expressed multiple soliton solutions in terms of quasideterminants and as ratios of ordinary determinants for NC and commutative NLSE in 2 + 1 dimensions, respectively. The quasideterminant formula for K-times repeated MDT enables us to compute single, double and triple soliton solutions for NC and commutative (2 + 1)-dimensional NLSE. Some interesting localized solutions are obtained for the NC and commutative NLSE in 2 + 1 dimensions.

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