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Symmetry
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Symmetry in Nonlinear Optics: Topics and Advances
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Symmetry in Nonlinear Optics: Topics and Advances

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 7133

Special Issue Editor

Dr. Yakup Yıldırım

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Arts and Sciences, Near East University, Nicosia 99138, Cyprus
Interests: solitons; conservation laws; symbolic computation; Lie symmetry analysis; analytics; numerics; integration methods; Korteweg-de Vries equation; nonlinear Schrödinger's equation; perturbation; maximum intensity; non-kerr law; refractive index; polarization

Special Issue Information

Dear Colleagues,

This Special Issue of Symmetry is devoted to recent developments in the theory of solitary waves and symmetries in nonlinear optics and its applications. 

One of the most important developments in nonlinear optics is the discovery and use of the soliton effect. Solitons or solitary waves are a specific kind of wave. Solitons are stable localized wave packets. Solitons propagate long distance in dispersive media without changing their shapes. Solitons propagate at a constant velocity. In addition, solitons are unaltered in shape and speed by a collision with other solitons. In nonlinear optics, an optical soliton refers to an optical field that does not change during propagation in consequence of a delicate balance between group velocity dispersion and nonlinearity effects. Optical soliton pulses are very useful for transmitting high data rate information in long-distance optical fiber communications. Therefore, optical solitons have been a substantial exploratory field. Consequently, the dynamics of soliton propagation has been extensively addressed in various kinds of optical waveguides.

The method of Lie symmetry is one of the most powerful methods for obtaining optical solitons with the governing models in nonlinear optics. In the last few decades, Lie’s method has been described in a number of excellent textbooks and has been applied to a number of physical and engineering models. The study of the group of infinitesimal transformations, in other words, Lie group point transformations, has an important place in this method. The Lie symmetry method, developed in the 19th century (1842–1899) by the Norwegian mathematician Sophus Lie, is exceptionally algorithmic. This method systematically combines and expands famous ad hoc methodologies for constructing optical solitons with the model equations in optical fiber communications. 

This Special Issue of Symmetry features articles about all aspects of Lie symmetry analysis, optical solitons, perturbation, non-Kerr law, polarization, birefringence, dense wavelength division multiplexed system, couplers, Bragg gratings, dispersive solitons, cubic-quartic solitons, highly dispersive solitons, pure-cubic solitons, and chirped solitons. 

Submit your paper and select the Journal “Symmetry” and the Special Issue “Solitary Waves and Symmetry in Nonlinear Optics: Topics and Advances” via the MDPI submission system. We look forward to your contributions to review and original research articles which deal with recent topics and advances in optical solitary waves and symmetry. The published papers in this Special Issue of Symmetry could provide crucial examples and possible new researches for further advancements. 

Please note that all submitted papers must be within the general scope of the Symmetry journal. 

Dr. Yakup Yıldırım
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Lie symmetry analysis
  • optical solitons
  • perturbation
  • non-Kerr law
  • polarization
  • birefringence
  • photonic crystal fibers
  • dense wavelength division multiplexed system
  • couplers
  • Bragg gratings

Published Papers (5 papers)

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Research

14 pages, 825 KiB  
Article
Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics
by Muslum Ozisik, Aydin Secer and Mustafa Bayram
Symmetry 2023, 15(1), 165; https://doi.org/10.3390/sym15010165 - 05 Jan 2023
Cited by 4 | Viewed by 1584
Abstract
We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows [...] Read more.
We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows the modeling of waves traveling in both directions and does not require the zero-mass assumption, which is necessary for many scientific applications. Considering these properties enables researchers to obtain more precise results in many physics and engineering applications, especially in research on the dynamics of water waves. We used the modified extended tanh function method (METFM) and Kudryashov’s method, which are easily applicable, do not require further mathematical manipulations, and give effective results to investigate the physical properties of the KP-B equation and its soliton solutions. As the output of the work, we obtained some new singular soliton solutions to the governed equation and simulated them with 3D and 2D graphs for the reader to understand clearly. These results and graphs describe the single and singular soliton properties of the (3+1)-dimensional KP-B equation that have not been studied and presented in the literature before, and the methods can also help in obtaining the solution to the evolution equations and understanding wave propagation in water wave dynamics. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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14 pages, 2230 KiB  
Article
Spectral Methods in Nonlinear Optics Equations for Non-Uniform Grids Using an Accelerated NFFT Scheme
by Pedro Rodríguez, Manuel Romero, Antonio Ortiz-Mora and Antonio M. Díaz-Soriano
Symmetry 2023, 15(1), 47; https://doi.org/10.3390/sym15010047 - 24 Dec 2022
Viewed by 1029
Abstract
In this work, we propose the use of non-homogeneous grids in 1D and 2D for the study of various nonlinear physical equations using spectral methods. As is well known, the use of spectral methods allow a faster resolution of the problem via the [...] Read more.
In this work, we propose the use of non-homogeneous grids in 1D and 2D for the study of various nonlinear physical equations using spectral methods. As is well known, the use of spectral methods allow a faster resolution of the problem via the application of the ubiquitous Fast Fourier Transform (FFT) algorithm. We will center our investigation on the search of fast and accurate schemes to solve the spectral operators in the Fourier space. In particular, we will use the Conjugate Gradient (CG) iterative method, with a preconditioning matrix to accelerate the inversion process of the non-uniform Fast Fourier Transform (NFFT). As it will be shown, the results obtained are in good agreement with the expected values. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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14 pages, 15762 KiB  
Article
Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations
by Pengfei Li, Yanzhu Wei, Boris A. Malomed and Dumitru Mihalache
Symmetry 2022, 14(12), 2664; https://doi.org/10.3390/sym14122664 - 16 Dec 2022
Cited by 3 | Viewed by 1427
Abstract
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values 1≤α≤2. [...] Read more.
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values 1≤α≤2. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance, ζ. The management format with the nonlinearity coefficient decaying as 1/ζ is considered too. These management schemes maintain stable propagation of the ring-Airy beams, which maintain their axial symmetry, in contrast to the symmetry-breaking splitting instability of ring-shaped patterns in 2D Kerr media. The instability driven by supercritical collapse at all values α<2 in the presence of the self-focusing cubic term is eliminated, too, by the means of management. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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28 pages, 3583 KiB  
Article
Deflection Analysis of a Nonlocal Euler–Bernoulli Nanobeam Model Resting on Two Elastic Foundations: A Generalized Differential Quadrature Approach
by Ramzy M. Abumandour, Mohammed A. El-Shorbagy, Islam M. Eldesoky, Mohamed H. Kamel, Hammad Alotaibi and Ahmed L. Felila
Symmetry 2022, 14(11), 2342; https://doi.org/10.3390/sym14112342 - 07 Nov 2022
Cited by 1 | Viewed by 1224
Abstract
This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear [...] Read more.
This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear forces, by considering various boundary conditions’ effects. The governing formulations are determined numerically by the Generalized Differential Quadrature Method (GDQM). A deep search is used to analyze parameters—such as the nonlocal (scaling effect) parameter, nonuniformity of area, the presence of two linear elastic foundations (Winkler–Pasternak elastic foundations), axial force, and the distributed load on the nanobeam’s deflection—with three different types of supports. The significant deductions can be abbreviated as follows: It was found that the nondimensional deflection of the nanobeam was fine while decreasing the scaling effect parameter of the nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional deflection increases when increasing the scaling effect parameter. Conversely, when the nanobeam is resting on an elastic foundation, the nondimensional deflection of the nanobeam decreases as the scaling effect parameter is increased. In addition, when the cross-sectional area of the nanobeam varies parabolically, the nondimensional deflection of the nonuniform nanobeam decreases in comparison to when the cross-sectional area varies linearly. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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20 pages, 6984 KiB  
Article
Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition
by Hassan Almusawa, Adil Jhangeer and Maham Munawar
Symmetry 2022, 14(7), 1377; https://doi.org/10.3390/sym14071377 - 04 Jul 2022
Cited by 6 | Viewed by 1191
Abstract
This research explores the solitary wave solutions, including dynamic transitions for a fractional low-pass electrical transmission (LPET) line model. The fractional-order (FO) LPET line mathematical system has yet to be published, and neither has it been addressed via the extended direct algebraic technique. [...] Read more.
This research explores the solitary wave solutions, including dynamic transitions for a fractional low-pass electrical transmission (LPET) line model. The fractional-order (FO) LPET line mathematical system has yet to be published, and neither has it been addressed via the extended direct algebraic technique. A computer program is utilized to validate all of the incoming solutions. To illustrate the dynamical pattern of a few obtained solutions indicating trigonometric, merged hyperbolic, but also rational soliton solutions, dark soliton solutions, the representatives of the semi-bright soliton solutions, dark singular, singular solitons of Type 1 and 2, and their 2D and 3D trajectories are presented by choosing appropriate values of the solutions’ unrestricted parameters. The effects of fractionality and unrestricted parameters on the dynamical performance of achieved soliton solutions are depicted visually and thoroughly explored. We furthermore discuss the sensitivity assessment. We, however, still examine how our model’s perturbed dynamical framework exhibits quasi periodic-chaotic characteristics. Our investigated solutions are compared with those listed in published literature. This research demonstrates the approach’s profitability and effectiveness in extracting a range of wave solutions to nonlinear evolution problems in mathematics, technology, and science. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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