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Symmetry
Special Issues
Recent Developments and Applications in Nonlinear Optics
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Recent Developments and Applications in Nonlinear Optics

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 3116

Special Issue Editor

Prof. Dr. Mustafa Bayram

E-Mail Website
Guest Editor
Department of Computer Engineering, Biruni University, Istanbul, Turkey
Interests: differential equations; applied mathematics; computer engineering; computer algebra
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Symmetry is devoted to recent developments and applications in nonlinear optics.

One of the most important developments in nonlinear optics is the soliton effect. Solitons or solitary waves are a specific kind of wave. Solitons are stable localized wave packets. Solitons propagate long distances 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 represent a substantial exploratory field. Consequently, the dynamics of soliton propagation has been addressed in various kinds of optical waveguides. In order to reveal soliton solutions with governing equations in nonlinear optics, many integration methods have been proposed. One such method is Lie symmetry, which has been described in a number of excellent textbooks and has been applied to a number of physical and engineering models. The Lie symmetry method is exceptionally algorithmic. This method systematically combines famous methodologies for constructing soliton solutions in optical fiber communications. This Special Issue of Symmetry features articles about all aspects of Lie symmetry analysis in nonlinear optics.

Submit your paper and select the journal Symmetry and the Special Issue “Recent Developments and Applications in Nonlinear Optics” via the MDPI submission system. We look forward to receiving your contributions of review and original research articles that deal with recent topics and advances in nonlinear optics and symmetry. The published papers in this Special Issue of Symmetry could provide crucial examples and possible new research directions for further advancements.

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

Prof. Dr. Mustafa Bayram
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 soliton solutions
  • non-Kerr laws
  • integration methods
  • nonlinear Schrödinger's equation

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Published Papers (2 papers)

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Research

20 pages, 6121 KiB  
Article
Abundant Soliton Solutions to the Generalized Reaction Duffing Model and Their Applications
by Miguel Vivas-Cortez, Maryam Aftab, Muhammad Abbas and Moataz Alosaimi
Symmetry 2024, 16(7), 847; https://doi.org/10.3390/sym16070847 - 4 Jul 2024
Cited by 1 | Viewed by 850
Abstract
The main aim of this study is to obtain soliton solutions of the generalized reaction Duffing model, which is a generalization for a collection of prominent models describing various key phenomena in science and engineering. The equation models the motion of a damped [...] Read more.
The main aim of this study is to obtain soliton solutions of the generalized reaction Duffing model, which is a generalization for a collection of prominent models describing various key phenomena in science and engineering. The equation models the motion of a damped oscillator with a more complex potential than in basic harmonic motion. Two effective techniques, the mapping method and Bernoulli sub-ODE technique, are used for the first time to obtain the soliton solutions of the proposed model. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals, is applied, and a nonlinear ordinary differential equation form is derived. These approaches effectively retrieve a hyperbolic, Jacobi function as well as trigonometric solutions while the appropriate conditions are applied to the parameters. Numerous innovative solutions, including the kink wave, anti-kink wave, bell shape, anti-bell shape, W-shape, bright, dark and singular shape soliton solutions, were produced via the mapping and Bernoulli sub-ODE approaches. The research includes comprehensive 2D and 3D graphical representations of the solutions, facilitating a better understanding of their physical attributes and proving the effectiveness of the proposed methods in solving complex nonlinear equations. It is important to note that the proposed methods are competent, credible and interesting analytical tools for solving nonlinear partial differential equations. Full article
(This article belongs to the Special Issue Recent Developments and Applications in Nonlinear Optics)
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13 pages, 776 KiB  
Article
Kink Soliton Dynamic of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Equation via a Couple of Integration Techniques
by Hasan Cakicioglu, Muslum Ozisik, Aydin Secer and Mustafa Bayram
Symmetry 2023, 15(5), 1090; https://doi.org/10.3390/sym15051090 - 16 May 2023
Cited by 5 | Viewed by 1267
Abstract
In this article, the aim was to obtain kink soliton solutions of the (2+1)-dimensional integro-differential Jaulent–Miodek equation (IDJME), which is a prominent model related to energy-dependent Schrödinger potential and is used in fluid dynamics, condensed matter physics, optics and many engineering systems. The [...] Read more.
In this article, the aim was to obtain kink soliton solutions of the (2+1)-dimensional integro-differential Jaulent–Miodek equation (IDJME), which is a prominent model related to energy-dependent Schrödinger potential and is used in fluid dynamics, condensed matter physics, optics and many engineering systems. The IDJME is created depending on the parameters and with constant coefficients, and two efficient methods, the generalized Kudryashov and a sub-version of an auxiliary equation method, were applied for the first time. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals ∂∂x,∂∂y and ∂∂t, was applied, and a nonlinear ordinary differential equation (NODE) form was derived. In order to make physical interpretations, appropriate solution sets and soliton solutions were obtained by performing systematic operations in line with the algorithm of the proposed methods. Then, 3D, 2D and contour simulations were made. Interpretations of different kink soliton solutions were made by obtaining results that are consistent with previous studies in the literature. The obtained results contribute to the studies in this field, though the contribution is small. Full article
(This article belongs to the Special Issue Recent Developments and Applications in Nonlinear Optics)
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