scholarly journals New travelling wave solutions of the (1 + 1)-dimensional cubic nonlinear Schrodinger equation using novel (G′/G)-expansion method

2016 ◽  
Vol 5 (2) ◽  
pp. 109-118 ◽  
Author(s):  
M.G. Hafez
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Schrodinger Equation ◽  
Travelling Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Cubic Nonlinear Schrödinger Equation

Bifurcation Behaviour of the Travelling Wave Solutions of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

2011 ◽  
Vol 66 (12) ◽  
pp. 721-727 ◽  
Author(s):  
Zai-Yun Zhang ◽  
Xiang-Yang Gan ◽  
De-Ming Yu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Travelling Wave ◽  
Nonlinear Schrodinger Equation ◽  
Travelling Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity

In this paper, we study the bifurcations and dynamic behaviour of the travelling wave solutions of the perturbed nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity by using the theory of bifurcations of dynamic systems. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained

scholarly journals Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Heng Wang ◽  
Longwei Chen ◽  
Hongjiang Liu ◽  
Shuhua Zheng
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Travelling Wave ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Phase Portraits ◽  
Travelling Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

By using the method of dynamical system, the exact travelling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms are studied. Based on this method, all phase portraits of the system in the parametric space are given with the aid of the Maple software. All possible bounded travelling wave solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic travelling wave solutions, are obtained, respectively. The results presented in this paper improve the related previous conclusions.

scholarly journals Optical Solitons and Other Solutions to the (2+1)-Dimensional Cubic Nonlinear Schrödinger Equation with Fractional Temporal Evolution

2018 ◽  
Vol 22 ◽  
pp. 01053
Author(s):  
Sibel Sehriban Atas ◽  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Temporal Evolution ◽  
Nonlinear Partial Differential Equation ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Cubic Nonlinear Schrödinger Equation

In this study, the (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution is investigated by using the extended sinh-Gordon equation expansion method. The idea of conformable fractional derivative is used in transforming the complex nonlinear partial differential equation to nonlinear ordinary differential equation. Dark, bright, mixed dark-bright, singular, mixed singular solitons and singular periodic wave solutions are successfully reached. The parametric conditions for the existence of valid solitons are given. The 2D and 3D graphics to some of the reported solutions are plotted.

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