scholarly journals ON THE LOCATION OF SPIKES FOR THE SCHRÖDINGER EQUATION WITH ELECTROMAGNETIC FIELD

2005 ◽  
Vol 07 (02) ◽  
pp. 251-268 ◽  
Author(s):  
SIMONE SECCHI ◽  
MARCO SQUASSINA
Keyword(s):  
Electromagnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
External Electromagnetic Field ◽  
Power Type ◽  
Wave Solutions ◽  
Semilinear Schrödinger Equation ◽  
Ground Energy

We consider the standing wave solutions of the three dimensional semilinear Schrödinger equation with competing potential functions V and K and under the action of an external electromagnetic field B. We establish some necessary conditions for a sequence of such solutions to concentrate, in two different senses, around a given point. In the particular but important case of nonlinearities of power type, the spikes locate at the critical points of a smooth ground energy map independent of B.

Diverse bistable dark novel explicit wave solutions of cubic–quintic nonlinear Helmholtz model

2021 ◽  
pp. 2150441
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
General Model ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Computational Schemes ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

Some novel optical solutions to the perturbed nonlinear Schrödinger model arising in nano-fibers mechanical systems

2021 ◽  
Author(s):  
Onur Alp Ilhan ◽  
Jalil Manafian ◽  
Mehrdad Lakestani ◽  
Gurpreet Singh
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
First Time

This paper aims to compute solitary wave solutions and soliton wave solutions based on the ansatz methods to the perturbed nonlinear Schrödinger equation (NLSE) arising in nano-fibers. The improved [Formula: see text]-expansion method and the rational extended sinh–Gordon equation expansion method are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accuracy interpretation of the propagation of solitons. We held a comparison between our results and those are in the previous work. The outcome indicates that perturbed NLSE arising nano-fibers is used in optical problems. Finally, via symbolic computation, their dynamic structure and physical properties were vividly shown by three-dimensional, density, and [Formula: see text]-curves plots. These solutions have greatly enriched the exact solutions of (2+1)-dimensional perturbed nonlinear Schrödinger equation in the existing literatures.

Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 675-681
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Equation Method ◽  
Direct Integration ◽  
Wave Solutions ◽  
Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

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