Optical solitons to the (n + 1)-dimensional nonlinear Schrödinger’s equation with Kerr law and power law nonlinearities using two integration schemes

In this study, two integration techniques are employed to reach optical solitons to the [Formula: see text]-dimensional nonlinear Schrödinger’s equation [Formula: see text]-NLSE[Formula: see text] with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.

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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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New soliton solutions for resonant nonlinear Schrödinger’s equation having full nonlinearity

International Journal of Modern Physics B ◽

10.1142/s0217979220500320 ◽

2020 ◽

Vol 34 (06) ◽

pp. 2050032 ◽

Cited By ~ 1

Author(s):

Khalid K. Ali ◽

Hadi Rezazadeh ◽

R. A. Talarposhti ◽

Ahmet Bekir

Keyword(s):

Power Law ◽

Soliton Solutions ◽

Schrödinger’S Equation ◽

Modified Kudryashov Method ◽

Cubic Law ◽

Kudryashov Method ◽

Full Nonlinearity ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

In this paper, we discuss deep visual solutions of resonant nonlinear Schrödinger’s equation having full nonlinearity via taking the modified Kudryashov method. There are four types of nonlinearity in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law and triple-power law. By performing this algorithm, logarithmical and rational solitons are deduced.

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OPTICAL SOLITONS WITH DUAL-POWER LAW NONLINEARITY USING LIE SYMMETRIES

Modern Physics Letters B ◽

10.1142/s0217984910024201 ◽

2010 ◽

Vol 24 (17) ◽

pp. 1833-1838 ◽

Cited By ~ 4

Author(s):

C. MASOOD KHALIQUE ◽

ANJAN BISWAS

Keyword(s):

Power Law ◽

Soliton Solution ◽

Optical Solitons ◽

Lie Symmetry ◽

Lie Symmetries ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation ◽

Dual Power

This paper obtains the stationary optical 1-soliton solution of the nonlinear Schrödinger's equation with dual-power law nonlinearity. The technique of Lie symmetry is used to obtain the solution.

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Optical Solitons with Coupled Nonlinear Schrodinger’s Equation in Birefringent Nano-Fibers by Adomian Decomposition Method

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2016.5444 ◽

2016 ◽

Vol 13 (8) ◽

pp. 5493-5498 ◽

Cited By ~ 6

Author(s):

A. A. Al Qarni ◽

M. A Banaja ◽

H. O Bakodah ◽

Mohammad Mirzazadeh ◽

Biswas Anjan

Keyword(s):

Decomposition Method ◽

Adomian Decomposition Method ◽

Optical Solitons ◽

Schrödinger’S Equation ◽

Adomian Decomposition ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

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Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity

Modern Physics Letters B ◽

10.1142/s0217984919501586 ◽

2019 ◽

Vol 33 (13) ◽

pp. 1950158 ◽

Cited By ~ 7

Author(s):

Nauman Raza ◽

Asad Zubair

Keyword(s):

Optical Fibers ◽

Soliton Solutions ◽

Algebraic Method ◽

Rational Solutions ◽

Schrödinger’S Equation ◽

Light Pulses ◽

Propagation Of Light ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

This work is devoted to scrutinize new optical soliton solutions to the spatially temporal [Formula: see text]-dimensional nonlinear Schrödinger’s equation (NLSE) with anti-cubic nonlinearity. Two different versatile integration architectures are used to extract these solitons. Extended direct algebraic method (EDAM) is utilized to pluck out optical, dark and singular soliton solutions, whereas generalized Kudryashov method (GKM) provides rational solutions. The fetched results are new and useful for the propagation of light pulses in optical fibers in [Formula: see text]-dimensions. For the existence of these solitons, constraint conditions are also listed.

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Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity

Optik ◽

10.1016/j.ijleo.2014.04.014 ◽

2014 ◽

Vol 125 (16) ◽

pp. 4246-4256 ◽

Cited By ~ 48

Author(s):

M. Mirzazadeh ◽

M. Eslami ◽

B. Fathi Vajargah ◽

Anjan Biswas

Keyword(s):

Power Law ◽

Optical Solitons ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear 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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Optical Solitons and Their Numerical Simulations of Coupled Nonlinear Schrödinger’s Equation in a Cascaded System

Simulation Tools and Techniques - Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering ◽

10.1007/978-3-030-72792-5_32 ◽

2021 ◽

pp. 391-401

Author(s):

Dahe Feng

Keyword(s):

Numerical Simulations ◽

Optical Solitons ◽

Schrödinger’S Equation ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation ◽

Cascaded System

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Multiple soliton solutions with chiral nonlinear Schrödinger’s equation in (2+1)-dimensions

European Journal of Mechanics - B/Fluids ◽

10.1016/j.euromechflu.2020.07.014 ◽

2021 ◽

Vol 85 ◽

pp. 68-75 ◽

Cited By ~ 3

Author(s):

Aziz Ullah Awan ◽

Muhammad Tahir ◽

Kashif Ali Abro

Keyword(s):

Soliton Solutions ◽

Schrödinger’S Equation ◽

Multiple Soliton Solutions ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

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Chiral solitons of the (1 + 2)-dimensional nonlinear Schrodinger’s equation

Modern Physics Letters B ◽

10.1142/s0217984919504013 ◽

2019 ◽

Vol 33 (32) ◽

pp. 1950401 ◽

Cited By ~ 1

Author(s):

Ahmad Javid ◽

Nauman Raza

Keyword(s):

Soliton Solutions ◽

Expansion Method ◽

Simple Equation ◽

Schrödinger’S Equation ◽

Modified Simple Equation Method ◽

Singular Soliton ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Chiral Solitons ◽

Nonlinear Schrödinger’S Equation

In this work, dark and singular soliton solutions of the (1[Formula: see text]+[Formula: see text]2)-dimensional chiral nonlinear Schrödinger’s equation are obtained and analyzed dynamically along with graphical depictions. The extraction of these chiral solitons is carried out using two integration tools such as the modified simple equation method and the [Formula: see text]-expansion method. The validity conditions for the existence of these solitons are also retrieved. It is highlighted that the solitons retrieved here are of chiral nature.

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