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.

Highly dispersive optical soliton perturbation with cubic–quintic–septic law via two methods

2021 ◽  
pp. 2150276
Author(s):  
Khalid K. Ali ◽  
Hadi Rezazadeh ◽  
Nauman Raza ◽  
Mustafa Inc
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Mixed Complex ◽  
Solitary Wave Solutions ◽  
Computational System ◽  
Soliton Perturbation ◽  
Wave Solutions

The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena.

scholarly journals Statistical dynamics of dual-power law optical soliton

2008 ◽  
Vol 21 (1) ◽  
pp. 37-44
Author(s):  
Anjan Biswas
Keyword(s):  
Perturbation Theory ◽  
Optical Fiber ◽  
Power Law ◽  
Langevin Equation ◽  
Stochastic Perturbation ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Statistical Dynamics ◽  
Soliton Perturbation ◽  
Dual Power

The dynamics of optical solitons with dual-power law nonlinearity, in presence of a stochastic perturbation term, is studied in this paper. The soliton perturbation theory is exploited to obtain the Langevin equation by virtue of which one can conclude that solitons travel down the optical fiber with a fixed mean free velocity. .

Highly dispersive optical soliton perturbation of Kudryashov’s arbitrary form having sextic-power law refractive index

2021 ◽  
Vol 35 (24) ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Refractive Index ◽  
Power Law ◽  
Soliton Solutions ◽  
Research Paper ◽  
Optical Soliton ◽  
Integration Scheme ◽  
Arbitrary Form ◽  
Soliton Perturbation ◽  
Singular Soliton ◽  
Simple Integration

In this research paper, a simple integration scheme is executed to secure new dark and singular soliton solutions for the highly dispersive nonlinear Schrödinger’s equation having Kudryashov’s arbitrary form with generalized nonlocal laws and sextic-power law refractive index.

Pure-cubic optical soliton perturbation with full nonlinearity by unified Riccati equation expansion

Optik ◽  
2020 ◽  
Vol 223 ◽  
pp. 165445 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Mohamed E.M. Alngar ◽  
Anjan Biswas ◽  
Mir Asma ◽  
Mehmet Ekici ◽  
...  
Keyword(s):  
Riccati Equation ◽  
Optical Soliton ◽  
Soliton Perturbation ◽  
Full Nonlinearity

Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation

2019 ◽  
Vol 20 (3-4) ◽  
pp. 441-448
Author(s):  
Chaonan Duan ◽  
Fajun Yu ◽  
Mengzhe Tian
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Dynamic Features ◽  
Hirota Equation ◽  
Elastic Interactions ◽  
Bright Solitons ◽  
Wave Characteristics ◽  
Determinant Representation ◽  
Local Case ◽  
Nonlocal Nonlinear

AbstractThe generalized nonlocal nonlinear Hirota (GNNH) equation has been widely concerned, it can be regarded as the generalization of the nonlocal Schrödinger equation, and can be reduced to a nonlocal Hirota equation. In this paper, we mainly study a GNNH equation and its determinant representation of the N-fold Darboux transformation. Then we derive some novel exact solutions including the breather wave solitons, bright solitons, some characteristics of solitary wave and interactions are considered. In particularly, the dynamic features of one-soliton, two-soliton solutions and the elastic interactions between the two solitons are displayed. We find that unlike the local case, the q(x,t) and $q^{*}(-x,t)$ of the GNNH equation have some novel characteristics of solitary wave, which are different form the classical Hirota equation.

Optical soliton perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method

Optik ◽  
2018 ◽  
Vol 157 ◽  
pp. 1214-1218 ◽  
Author(s):  
Anjan Biswas ◽  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Houria Triki ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Optical Soliton ◽  
Equation Method ◽  
Trial Equation Method ◽  
Soliton Perturbation ◽  
Full Nonlinearity

QUASI-STATIONARY SOLITONS FOR LANGMUIR WAVES IN PLASMAS WITH FULL NONLINEARITY

2011 ◽  
Vol 03 (04) ◽  
pp. 217-227 ◽  
Author(s):  
SAMI ATIF ◽  
ANJAN BISWAS ◽  
ESSAID ZERRAD
Keyword(s):  
Perturbation Theory ◽  
Power Law ◽  
Higher Order ◽  
Langmuir Waves ◽  
Additional Information ◽  
Soliton Perturbation ◽  
Definition Of ◽  
Full Nonlinearity ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation

The quasi-stationary solitons for Langmuir waves in plasmas is obtained in this paper. This model is governed by the perturbed nonlinear Schrödinger's equation with cubic and power law nonlinearities. The perturbation terms are considered with full nonlinearity. A new generalized definition of the phase of the soliton is introduced. This leads to additional information at higher order level which soliton perturbation theory fails to capture.

scholarly journals Cubic-quartic optical soliton perturbation with Fokas–Lenells equation by semi-inverse variation

2021 ◽  
Vol 24 (04) ◽  
pp. 431-435
Author(s):  
A. Biswas ◽  
◽  
A. Dakova ◽  
S. Khan ◽  
M. Ekici ◽  
...  
Keyword(s):  
Variational Principle ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Soliton Perturbation ◽  
Hamiltonian Perturbation

This paper recovers cubic-quartic bright optical solitons with perturbed Fokas–Lenells equation. The Hamiltonian perturbation terms appear with maximal permissible intensity. The semi-inverse variational principle is employed to retrieve such solitons.

scholarly journals Optical soliton perturbation and conservation law with Kudryashov’s refractive index having quadrupled power-law and dual form of generalized nonlocal nonlinearity

2021 ◽  
Vol 24 (1) ◽  
pp. 64-70
Author(s):  
Y. Yildirim ◽  
◽  
A. Biswas ◽  
A.H. Kara ◽  
M. Ekici ◽  
...  
Keyword(s):  
Refractive Index ◽  
Power Law ◽  
Nonlinear Refractive Index ◽  
Conservation Law ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Complete Picture ◽  
Nonlocal Nonlinearity ◽  
Dual Form ◽  
Soliton Perturbation

This paper is devoted to optical solitons for Kudryashov’s law of nonlinear refractive index, which stem from quadrupled-power law and dual form of nonlocal nonlinearity. The conservation law has been also exhibited to paint a complete picture of the model.

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