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.

Soliton Solutions, Conservation Laws, and Reductions of Certain Classes of NonlinearWave Equations

2012 ◽  
Vol 67 (10-11) ◽  
pp. 613-620 ◽  
Author(s):  
Richard Morris ◽  
Abdul Hamid Kar ◽  
Abhinandan Chowdhury ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Nonlinear Wave Equations ◽  
Conserved Quantities ◽  
Symmetry Approach ◽  
Lie Symmetry Approach

In this paper, the soliton solutions and the corresponding conservation laws of a few nonlinear wave equations will be obtained. The Hunter-Saxton equation, the improved Korteweg-de Vries equation, and other such equations will be considered. The Lie symmetry approach will be utilized to extract the conserved densities of these equations. The soliton solutions will be used to obtain the conserved quantities of these equations.

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.

On symmetries, reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion

Optik ◽  
2013 ◽  
Vol 124 (21) ◽  
pp. 5116-5123 ◽  
Author(s):  
R. Morris ◽  
P. Masemola ◽  
A.H. Kara ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Optical Solitons ◽  
Conserved Quantities ◽  
Modal Dispersion

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.

Dispersive optical solitons with Schrödinger–Hirota equation

2014 ◽  
Vol 23 (01) ◽  
pp. 1450014 ◽  
Author(s):  
A. H. Bhrawy ◽  
A. A. Alshaery ◽  
E. M. Hilal ◽  
Wayne N. Manrakhan ◽  
Michelle Savescu ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Hirota Equation ◽  
Bright Solitons ◽  
Soliton Perturbation ◽  
Full Nonlinearity

The dynamics of dispersive optical solitons, modeled by Schrödinger–Hirota equation, are studied in this paper. Bright, dark and singular optical soliton solutions to this model are obtained in presence of perturbation terms that are considered with full nonlinearity. Soliton perturbation theory is also applied to retrieve adiabatic parameter dynamics of bright solitons. Optical soliton cooling is also studied. Finally, exact bright, dark and singular solitons are addressed for birefringent fibers with perturbation terms included.

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.

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.

scholarly journals Solitons: Conservation laws and dressing methods

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1930003
Author(s):  
Anastasia Doikou ◽  
Iain Findlay
Keyword(s):  
Conservation Laws ◽  
Riccati Equation ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Soliton Solutions ◽  
Toda Chain ◽  
Lax Pair ◽  
Conserved Quantities ◽  
Nonlinear Schrödinger ◽  
Marchenko Equation

We review some of the fundamental notions associated with the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary differential equations that are associated to discrete or continuous integrable systems. The Riccati equation associated to a given continuous integrable system is also solved and hence suitable conserved quantities are derived. The notion of the Darboux–Bäcklund transformation is introduced and employed in order to obtain soliton solutions for specific examples of integrable equations. The Zakharov–Shabat dressing scheme and the Gelfand–Levitan–Marchenko equation are also introduced. Via this method, generic solutions are produced and integrable hierarchies are explicitly derived. Various discrete and continuous integrable models are employed as examples such as the Toda chain, the discrete nonlinear Schrödinger model, the Korteweg–de Vries and nonlinear Schrödinger equations as well as the sine-Gordon and Liouville models.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

Sign in / Sign up

Export Citation Format

Share Document