scholarly journals Wellposedness and Asymptotic Behavior of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity and Localized Damping

2020 ◽  
Vol 63 (3) ◽  
pp. 293-322
Author(s):  
Zaiyun Zhang ◽  
Zhenhai Liu ◽  
Mingbao Sun
Keyword(s):  
Asymptotic Behavior ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Localized Damping

scholarly journals Non topological 1-soliton solution to resonant nonlinear schrodinger equation with kerr law nonlinearity

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Salam Subhaschandra Singh
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Schrödinger ◽  
Kerr Law ◽  
Kerr Law Nonlinearity

In this paper, using the methods of ansatz, sine-cosine and He’s semi-inverse variation, non-topological 1-soliton solution to Resonant Nonlinear Schrodinger Equation with Kerr law nonlinearity is obtained. The results show that these methods are very effective ones for finding exact solutions to various types of nonlinear evolution equations appearing in the studies of science and engineering.

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

Optical Solitons for the Perturbed Nonlinear Schrödinger Equation with Kerr Law and Non-Kerr Law Nonlinearity

2018 ◽  
Vol 73 (4) ◽  
pp. 315-321 ◽  
Author(s):  
Hui Gao ◽  
Tianzhou Xu ◽  
Gangwei Wang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Integration Schemes ◽  
Kerr Law ◽  
Special Cases ◽  
Kerr Law Nonlinearity

AbstractThis paper analyses the dynamics of soliton propagation through optical fibres for the perturbed nonlinear Schrödinger equation with Kerr law and non-Kerr law nonlinearity. Several integration schemes are used to construct solitons to the model. The two forms of nonlinearity that are studied in detail are power law and dual power law, while Kerr law and parabolic law emerge as special cases to these two laws.

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