Dynamics of new optical solitons for the Triki–Biswas model using beta-time derivative

2021 ◽  
Author(s):  
Asim Zafar ◽  
Ahmet Bekir ◽  
M. Raheel ◽  
Kottakkaran Sooppy Nisar ◽  
Salman Mustafa
Keyword(s):  
Model Equation ◽  
Pulse Propagation ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Integration Schemes ◽  
Ultrashort Pulse Propagation ◽  
Different Types ◽  
Efficient Integration ◽  
Derivative Nonlinear Schrödinger Equation

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation.

Propagation of diverse ultrashort pulses in optical fiber to Triki–Biswas equation and its modulation instability analysis

2021 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Abdullahi Yusuf ◽  
Bashir Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Optical Fiber ◽  
Model Equation ◽  
Pulse Propagation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Ultrashort Pulses ◽  
Optical Soliton ◽  
Integration Scheme ◽  
Efficient Integration ◽  
Complex Models

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations.

Optical solitons in dual core fibers under various nonlinearities

2019 ◽  
Vol 33 (17) ◽  
pp. 1950189 ◽  
Author(s):  
Syed Tahir Raza Rizvi ◽  
Kashif Ali ◽  
Haroon Hanif
Keyword(s):  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Optical Solitons ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Kerr Law ◽  
Cubic Law ◽  
Different Types ◽  
Log Law ◽  
Dual Core

This paper retrieves different types of soliton solutions for coupled nonlinear Schrödinger equation (NLSE). We use extended F-expansion method to find bright, dark and other trigonometric solutions with Kerr law and anti-cubic law. We also find Gausson soliton for coupled NLSE under log law nonlinearity.

scholarly journals Optical Solutions in Fiber Bragg Gratings with Polynomial Law Nonlinearity and Cubic-Quartic Dispersive Reflectivity-=SUP=-*-=/SUP=-

2021 ◽  
Vol 129 (11) ◽  
pp. 1409
Author(s):  
Elsayed M.E. Zayed ◽  
Mohamed E.M. Alngar ◽  
Anjan Biswas ◽  
Mehmet Ekici ◽  
Padmaja Guggilla ◽  
...  
Keyword(s):  
Refractive Index ◽  
Periodic Solutions ◽  
Nonlinear Refractive Index ◽  
Fiber Bragg Gratings ◽  
Soliton Solutions ◽  
Bragg Gratings ◽  
Optical Solitons ◽  
Auxiliary Equation ◽  
Equation Approach ◽  
Integration Schemes

Optical solitons with ber Bragg gratings and polynomial law of nonlinear refractive index are addressed in the paper. The auxiliary equation approach together with an addendum to Kudryashov's method identify soliton solutions to the model. Singular periodic solutions emerge from these integration schemes as a byproduct. Keywords: solitons; cubic-quartic; Bragg gratings.

scholarly journals Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 393
Author(s):  
S. Tuluce Demiray ◽  
U. Bayrakci
Keyword(s):  
Spin Chain ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Bright Soliton ◽  
Integration Schemes ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Chain Equation

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.

scholarly journals The conformable space–time fractional Fokas–Lenells equation and its optical soliton solutions based on three analytical schemes

2020 ◽  
pp. 2150004
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Ahmet Bekir ◽  
Waseem Razzaq
Keyword(s):  
Optical Fibers ◽  
Function Method ◽  
Pulse Propagation ◽  
Soliton Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Nonlinear Wave Propagation ◽  
Different Types ◽  
Hyperbolic Function Method ◽  
Exact Soliton Solutions

This paper is about the study of space–time fractional Fokas–Lenells equation that describes nonlinear wave propagation in optical fibers. Three prominent schemes are employed for extracting different types of exact soliton solutions. In particular, the [Formula: see text] function method, the hyperbolic function method and the simplest Riccati equation scheme are investigated for the said model. As a sequel, a series of soliton solutions are obtained and verified through MATHEMATICA. The obtained solutions are significant additions in some specific fields of physics and engineering. Furthermore, the 3D graphical descriptions are left to analyze the pulse propagation for the reader.

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

2019 ◽  
Vol 33 (19) ◽  
pp. 1950224 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Mustafa Bayram ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Power Laws ◽  
Optical Solitons ◽  
Schrödinger’S Equation ◽  
Integration Schemes ◽  
Undetermined Coefficient ◽  
Integration Techniques ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

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.

Cubic–quartic polarized optical solitons and conservation laws for perturbed Fokas–Lenells model

2021 ◽  
pp. 2150005
Author(s):  
Elsayed M. E. Zayed ◽  
Mohamed E. M. Alngar ◽  
Mahmoud M. El-Horbaty ◽  
Anjan Biswas ◽  
Abdul H. Kara ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Conserved Quantities ◽  
Bright Solitons ◽  
Integration Schemes

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach.

scholarly journals Different soliton solutions to the modified equal-width wave equation with Beta-time fractional derivative via two different methods

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Different Types ◽  
Non Linear ◽  
Time Fractional Derivative

‎In this paper‎, ‎different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as‎: ‎extended Jacobi's elliptic expansion function method and Kudryashov method‎. ‎The dark‎, ‎bright‎, ‎singular and other solitons are achieved‎. ‎The obtained soliton solutions are verified through MATHEMATICA‎. ‎At the end‎, ‎the results are also explained through graphs‎. ‎These soliton solutions suggest that these two methods are effective‎, ‎straight forward and reliable as compare to other methods‎. ‎The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures‎.

scholarly journals Optical Solitons in Bragg Gratings Fibers for The Nonlinear (2+1)-Dimensional Kundu-Mukherjee-Naskar Equation Using Two Integration Schemes

2021 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Reham Shohib ◽  
Mohamed E. M. Alngar
Keyword(s):  
Fiber Bragg Gratings ◽  
Soliton Solutions ◽  
Bragg Gratings ◽  
Optical Solitons ◽  
Current Work ◽  
Integration Schemes ◽  
First Time ◽  
Singular Soliton

Abstract The current work handles for the first time, dispersive optical solitons in fiber Bragg gratings for the nonlinear (2+1)-dimensional Kundu-Mukherjee-Naskar equation. Two integration schemes, namely, the modified Kudryashov's approach and the addendum to Kudryashov's methodology are applied. Dark, bright and singular soliton solutions are obtained. Also, combo bright-singular soliton solutions are introduced.

Sign in / Sign up

Export Citation Format

Share Document