On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

AbstractThis paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE) with time dependent coefficients.

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Optical solitons for the resonant nonlinear Schrödinger's equation with time-dependent coefficients by the first integral method

Optik ◽

10.1016/j.ijleo.2014.01.013 ◽

2014 ◽

Vol 125 (13) ◽

pp. 3107-3116 ◽

Cited By ~ 86

Author(s):

M. Eslami ◽

M. Mirzazadeh ◽

B. Fathi Vajargah ◽

Anjan Biswas

Keyword(s):

Integral Method ◽

First Integral ◽

Optical Solitons ◽

Time Dependent ◽

First Integral Method ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

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On optical solitons of the resonant Schrödinger’s equation in optical fibers with dual-power law nonlinearity and time-dependent coefficients

Waves in Random and Complex Media ◽

10.1080/17455030.2015.1028579 ◽

2015 ◽

Vol 25 (3) ◽

pp. 334-341 ◽

Cited By ~ 20

Author(s):

Bulent Kilic ◽

Mustafa Inc

Keyword(s):

Optical Fibers ◽

Power Law ◽

Optical Solitons ◽

Time Dependent ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Dual Power

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Numerical solution of the one-dimensional time-independent Schrödinger’s equation by recursive evaluation of derivatives

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.01.002 ◽

2010 ◽

Vol 215 (12) ◽

pp. 4400-4405 ◽

Cited By ~ 6

Author(s):

Asai Asaithambi

Keyword(s):

Numerical Solution ◽

One Dimensional ◽

Schrödinger’S Equation ◽

The One ◽

Recursive Evaluation ◽

Schrödinger's Equation

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A pedagogical extension of the one-dimensional Schrödinger’s equation to symmetric proximity effect system film sandwiches

AIP Advances ◽

10.1063/5.0074837 ◽

2022 ◽

Vol 12 (1) ◽

pp. 015015

Author(s):

B. J. Luke ◽

P. R. Broussard

Keyword(s):

Proximity Effect ◽

One Dimensional ◽

Schrödinger’S Equation ◽

The One ◽

Schrödinger's Equation

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Pedagogical applications of the one-dimensional Schrödinger’s equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions

American Journal of Physics ◽

10.1119/1.3078414 ◽

2009 ◽

Vol 77 (4) ◽

pp. 360-364 ◽

Cited By ~ 1

Author(s):

P. R. Broussard

Keyword(s):

Boundary Conditions ◽

Proximity Effect ◽

Neumann Boundary ◽

Neumann Boundary Conditions ◽

One Dimensional ◽

Schrödinger’S Equation ◽

The One ◽

Schrödinger's Equation

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Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time-dependent coefficients by simplest equation approach

Journal of Modern Optics ◽

10.1080/09500340.2013.850777 ◽

2013 ◽

Vol 60 (19) ◽

pp. 1627-1636 ◽

Cited By ~ 78

Author(s):

M. Eslami ◽

M. Mirzazadeh ◽

Anjan Biswas

Keyword(s):

Optical Fibers ◽

Soliton Solutions ◽

Time Dependent ◽

Equation Approach ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

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A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation

Mathematics ◽

10.3390/math7111124 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1124 ◽

Cited By ~ 1

Author(s):

Saleem Obaidat ◽

Said Mesloub

Keyword(s):

Stability Analysis ◽

Linear Method ◽

Phase Lag ◽

One Dimensional ◽

Schrödinger’S Equation ◽

First Derivative ◽

Algebraic Order ◽

The One ◽

Schrödinger's Equation ◽

Symmetric Method

In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Schrödinger’s equation. The error and stability analysis are studied. Also, the new method is compared with other methods in the literature. It is found that this method is more efficient than these methods.

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Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach

Nonlinear Dynamics ◽

10.1007/s11071-015-1989-1 ◽

2015 ◽

Vol 81 (1-2) ◽

pp. 277-282 ◽

Cited By ~ 101

Author(s):

Mohammad Mirzazadeh ◽

A. H. Arnous ◽

M. F. Mahmood ◽

Essaid Zerrad ◽

Anjan Biswas

Keyword(s):

Soliton Solutions ◽

Time Dependent ◽

Trial Solution ◽

Solution Approach ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

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Exact Chirped Soliton Solutions for the One-Dimensional Gross– Pitaevskii Equation with Time-Dependent Parameters

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0070 ◽

2012 ◽

Vol 67 (3-4) ◽

pp. 141-146 ◽

Cited By ~ 1

Author(s):

Zhenyun Qina ◽

Gui Mu

Keyword(s):

Soliton Solution ◽

Soliton Solutions ◽

Einstein Condensate ◽

Time Dependent ◽

Pitaevskii Equation ◽

Zero Temperature ◽

One Dimensional ◽

Bose Einstein Condensate ◽

The One ◽

Bose Einstein

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

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