Optical Solutions Research Articles

Resonant optical soliton solutions for time-fractional nonlinear Schrödinger equation in optical fibers

In this paper, several new optical soliton solutions of the time-fractional generalized resonant nonlinear Schrödinger equation, relevant to pulse propagation in optical fibers, are constructed using the extended simplest equation approach. The new exact solutions are expressed in terms of hyperbolic functions, trigonometric functions, and rational functions. Further, two-dimensional, three-dimensional, and contour graphs of king-type, wave, dark–bright, bright, and bell-shaped optical soliton solutions are plotted to elucidate the significance of the time-fractional generalized resonant nonlinear Schrödinger equation using appropriate values of physical parameters. The dynamic behavior of the present solutions, incorporating the effect of the conformable fractional derivative, is depicted through two-dimensional graphs. The derived optical solutions are considered novel and have presumably not been previously reported in the literature.

Abundant optical solutions for the stochastic Schrödinger–Hirota equation in quantum mechanics, science and engineering

Abundant optical solutions for the stochastic Schrödinger–Hirota equation in quantum mechanics, science and engineering

Novel stochastic embedded solitons with quadratic nonlinear susceptibility in the presence of multiplicative noise

This paper addresses the modeling of optical systems with stochastic quadratic nonlinearity for the first time, a novel and challenging research area within nonlinear optics. By incorporating multiplicative white noise and quadratic nonlinear susceptibility, the study presents an innovative approach to recovering optical solutions. Leveraging the G′G -expansion method and extended Kudryashov’s method, new stochastic exact solutions are derived, encompassing bright, dark, singular, and trigonometric solitons. Graphical representations aid in understanding these solutions’ characteristics. Insights into the stochastic nature of optical solutions under various conditions are provided, offering valuable contributions to nonlinear optics and potential applications in telecommunications and materials science.

Exploring chaotic behavior of optical solitons in complex structured Conformable Perturbed Radhakrishnan-Kundu-Lakshmanan Model

In this research, we aim to construct and examine optical soliton solutions for the complex structured Conformable Perturbed Radhakrishnan-Kundu-Lakshmanan Model (CPRKLM) using the Generalized-Kudryashov-Auxiliry Jacobian Method (GKAJM). The current study is notable for its thorough examination and for shedding insight on the chaotic behavior of families of localized optical soliton. Through the creation of 3D and contour visualizations that effectively capture the chaotic behaviors shown by these solitons, we are able to demonstrate that the optical solitons exhibit two distinct forms of perturbations: axial and periodic. Our research stimulates improvements in data processing tools and optical equipment, with consequences for communication networks and nonlinear fiber optics. Through a deeper understanding of optical solitons and their applications, this work also makes a substantial contribution to the discipline of nonlinear optics.

Lie group analysis, solitary wave solutions and conservation laws of Schamel Burger’s equation

This paper presents a Lie group analysis of the Schamel Burger’s equation, notable for producing shock-type traveling waves in distinctive physical contexts. We determine the infinitesimal generators for this equation using the Lie group theory of differential equations. By applying Lie point symmetries, we establish commutation relations, the adjoint representation, and identify the optimal system of sub-algebras. Using elements from this optimal system, we perform symmetry reductions, resulting in various nonlinear ordinary differential equations (ODEs). Some of these reductions yield exact explicit solutions, while others necessitate the use of the new auxiliary equation method to obtain optical soliton solutions. We illustrate the dynamics of these soliton solutions graphically through both two and three-dimensional representations of wave structures. Additionally, we compute the conservation laws for the Schamel Burger’s equation by applying Ibragimov’s theorem, deriving conserved quantities corresponding to its point Lie symmetries. This analysis underscores our novel contribution, offering insights not previously explored in the literature.

Construction of bilinear Bäcklund transformation and complexitons for a newer form of Boussinesq equation describing shallow water waves

This research investigates the characteristics and attributes of a new (3+ 1)-dimensional Boussinesq equation that describes shallow water waves in higher dimensions. By utilizing the Hirota bilinear representation, a bilinear Bäcklund transformation is provided for the proposed model to get soliton solutions. Then, the extended transform rational function method is applied to calculate the complexitons type solutions. The results demonstrate various exact solutions with different structures, including periodic, singular, and bright solitons. Comprehensive graphical representations in 2D, 3D, and density plots are provided to highlight the physical properties of these solutions. Our approach is distinguished by the unique nature of the problem and the use of previously untested methods in this context, leading to many new and original optical soliton solutions. These results highlight the effectiveness of the proposed method in tackling nonlinear problems in engineering and the natural sciences, exceeding previous work found in the literature.

Optical soliton solutions of nonlinear differential Boussinesq water wave equation via two analytical techniques

In this article, we examine the optical soliton solutions of the 4th-order nonlinear Boussinesq water wave equation using the modified (G′/G2)− expansion and F-expansion methods. We utilize the similarity transformation to transform the partial differential form of the equation into an ordinary differential form. These techniques present a variety of solutions, including bright, dark, singular, dark-periodic, and singular-periodic soliton solutions. We plot the derived solutions in several profiles, such as 2D, 3D, and contour, to illustrate their physical appearance. The determined findings might be useful and have an enormous effect on the research of nonlinear phenomena in a variety of physical areas of science, like shallow water waves, acoustics, fluid dynamics, laser optics, communication systems, and heat transfer. The achieved results demonstrate the validity, applicability, and effectiveness of the presented method. We plot and validate the found solutions using the computational program MATHEMATICA.

Nonlinear optical encoding enabled by recurrent linear scattering

AbstractOptical information processing and computing can potentially offer enhanced performance, scalability and energy efficiency. However, achieving nonlinearity—a critical component of computation—remains challenging in the optical domain. Here we introduce a design that leverages a multiple-scattering cavity to passively induce optical nonlinear random mapping with a continuous-wave laser at a low power. Each scattering event effectively mixes information from different areas of a spatial light modulator, resulting in a highly nonlinear mapping between the input data and output pattern. We demonstrate that our design retains vital information even when the readout dimensionality is reduced, thereby enabling optical data compression. This capability allows our optical platforms to offer efficient optical information processing solutions across applications. We demonstrate our design’s efficacy across tasks, including classification, image reconstruction, keypoint detection and object detection, all of which are achieved through optical data compression combined with a digital decoder. In particular, high performance at extreme compression ratios is observed in real-time pedestrian detection. Our findings open pathways for novel algorithms and unconventional architectural designs for optical computing.

Nonuniformity of diffractive splitting and receiver-transmitter alignment for large-field-of-view hundred-beam-scale LiDAR

To meet the spatial perception requirements for autonomous ship navigation in common scenarios such as ocean navigation, port entry and exit, and lock passage, commercial vehicle-mounted LiDAR technology falls short of demands in aspects such as sensing distance, field of view, angular resolution, and spatial sampling density. This paper proposes a hundred-beam-scale LiDAR scheme based on large-field-of-view diffractive beam splitting and a fiber array for echo reception and presents an in-depth investigation of the angular nonuniformity of diffractive beam splitting and the microradian-scale alignment for such hundred-beam-scale large-field-of-view LiDAR. This paper considers a combination of split-beam transmission based on a high-order diffractive optical element (DOE) and echo reception based on a high-precision fiber-optic line array. The nonlinear angular characteristics of the DOE are deduced and analyzed for a large field of view. The units of the receiving fiber-optic array are designed to offset the influence of the angular nonlinearity of the DOE, ensuring high-precision receiver–transmitter alignment of the hundred-beam-scale LiDAR for beams at any order of diffraction and helping to reduce system errors. The above-described LiDAR system has undergone laboratory testing and practical engineering verification, and it provides a new optical solution for LiDAR systems at the hundred-beam scale with a large field of view, a small divergence angle, and high sampling density. The presented system achieves a registration accuracy of 66.5 μrad with 128 beams and a 10-degree field of view, greatly improving signal reception efficiency. Such LiDAR systems have a wide range of applications, including space docking, target identification, lunar and planetary exploration, and ground-based vehicle-mounted LiDAR.

Novel optical soliton solutions to nonlinear paraxial wave model

In this paper, we primarily focus on the nonlinear paraxial wave equation in Kerr media, a generalization of the nonlinear Schrödinger equation utilized to characterize the dynamics of optical beam propagation. By using three potent analytical methods, namely, the Sine-Gordon expansion method, the functional variable method, and the Bernoulli ([Formula: see text])-expansion method, numerous novel soliton solutions are derived. These solutions, comprising hyperbolic, trigonometric and exponential functions, represent significant additions to the field of optics. Furthermore, we elucidate the physical characteristics of these novel optical soliton solutions by presenting a series of three-dimensional (3D) and two-dimensional (2D) graphs with appropriate parameter values.

Optical characterization sensing method of TFBG sensor for battery electromotive force monitoring

In the past few years, fiber optic sensors have demonstrated an amazing ability to detect the state of charge (SOC) and electromotive force (EMF) inside a battery in real-time. However, it remains an enormous challenge to characterize the relationship between the spectral shift of the fiber sensor and the internal EMF change of the battery. Here, we propose a method to monitor the electrolyte during the battery discharge process using the integral spectrum of a tiny tilted fiber Bragg grating (TFBG) sensor. The relationship between the fiber optic transmission spectrum and battery EMF was established by using this method. The results show that a TFBG sensor implanted in a lead-acid battery enables rapid EMF detection with a sensitivity of 1.16 × 105 (nm·dBm) /V. This technology provides a fiber optic precision solution for battery operating conditions and has excellent potential for detecting battery failures using traditional EMF methods.

Analytical solutions of the space–time fractional Kundu–Eckhaus equation by using modified extended direct algebraic method

The study of soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) has gained prominence recently because of its ability to realistically recreate complex physical processes. Numerous mathematical techniques have been devised to handle the problem of NFPDEs where soliton solutions are difficult to obtain. Due to their accuracy in reproducing complex physical phenomena, soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) have recently attracted interest. Several mathematical techniques have been devised to tackle the difficult task of solving non-finite partial differential equations (NFPDEs) soliton. Studies of soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) have garnered increased attention recently due to its capacity to accurately represent complex physical processes. Due to the difficulty of obtaining soliton solutions, NFPDEs can be solved using a wide variety of mathematical methods. In this way, it facilitates the extraction of the recently found abundance of optical soliton solutions. To further understanding of the results, the study also includes contour and three-dimensional images that visually depict particular optical soliton solutions for particular parameter selections, suggesting the existence of different soliton structures in the nonlinear fractional Kundu–Eckhaus equation (NFKEE) region. It is shown that the proposed technique is quite powerful and effective in solving several nonlinear FDEs.

Various exact solutions to the time-fractional nonlinear Schrödinger equation via the new modified Sardar sub-equation method

We aim to investigates the nonlinear Schrödinger equation including time-fractional derivative in (3+1)-dimensions by considering cubic and quantic terms The modified Sardar sub-equation method is used that lead to the discovery of a unique class of optical solutions. To transform the suggested nonlinear equation into an ordinary differential equation, we applied wave transformations, resulting in a set of nonlinear equations that offer diverse solution scenarios. The derived solutions encompass dark, wave, bright, mixed dark-bright, bell-shape, kink-shape, and singular soliton solutions. To enhance our understanding of the dynamic behavior exhibited by these solitons under varying time parameter values, visual simulations through a variety of graphs is presented. Furthermore, a comprehensive comparison is conducted, exploring a range of values for the conformable fractional order parameter. This comparison aims to highlight on the influence of fractional order variations on the solutions, contributing valuable insights into the nuanced dynamics of the system. Overall, this study serves to advance our understanding of nonlinear processes, and its potential applications in real-life phenomena. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons.

Optical soliton solutions of the third-order nonlinear Schrödinger equation in the absence of chromatic dispersion

This research paper is dedicated to the investigation of the optical soliton solutions with the power law of self-phase modulation (SPM) and the third-order dispersion (TOD), completely neglecting the chromatic dispersion (CD). The aim is focused on two main points. First, obtaining the straddled soliton solution which permits us to have bright and singular soliton by applying the new Kudryashov (nKM) scheme which was recently introduced as a simple, effective, and reliable method. Second, to observe the influences of the TOD, SPM, and inter-modal dispersion (IMD) on pure-cubic optical soliton dynamics in the absence of the CD.

Analyzing optical soliton solutions in Kairat-X equation via new auxiliary equation method

The paper introduce a novel auxiliary equation method for the successful derivation of traveling wave solutions for the non-linear Kairat-X (K-X) equation. Along with other novel results, soliton, singular, triangular periodic, and doubly periodic topological solutions are among the solutions obtained. The study revisits the concept of optical solitary waves, enhancing our understanding of the model. Previous studies have already derived analytical solutions using diverse approaches, contributing to the discovery of new soliton solutions within this framework. These solutions are characterized through three-dimensional, contour plot, and two-dimensional profile analyses. Additionally, the impact of time on the propagation of wave patterns is explored. The outcomes show how well our suggested approach works to solve non-linear evolution equations by producing fresh, more thorough solutions, making it a powerful mathematical tool for doing so. Through this article, we elucidate how leveraging NAEM with the Kairat-X equation can lead to optimized optical systems, improved data transmission rates, and the evolution of nonlinear optics towards more efficient and reliable communication technologies.

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

In this study, we use analytical algorithms, specifically the auxiliary equation (AE) approach, the improved F-expansion method, and the modified Sardar sub-equation (MSSE) method to investigate complex wave structures for plentiful solutions associated with the fractional perturbed Gerdjikov-Ivanov (PGI) model with the M-fractional operator. The investigated model is a well-established mathematical model used to represent a variety of physical events in nonlinear dynamics and mathematical physics. By using the aforementioned techniques, we scrutinize some new optical wave solutions in the framework of dark, bright, periodic, combo, W-shaped, M-shape, V-shape, kink type, singular rational, exponential, trigonometric, and hyperbolic solutions. The acquired solutions address a wide range of optical solutions in the form of 3D plots, contour plots, and 2D plots, declaring the free parameters of such optical soliton solutions and comprehending their dynamic behavior. Also, the sensitive analysis of the selected model is analyzed. The main contribution of this study is to extract diverse solitary wave solutions of the adopted model. Some of the solutions are similar and some diverge from the previous solutions which justifies the novelty of the study. Finally, we discovered that the current technique provides a reliable instrument for investigating the analytic solutions of fractional differential equations. The proposed PGI model can be used to transmit ultra-fast pulses across optical fibers. This research goes beyond to the advancement of mathematical techniques for solving fractional differential equations and broadens their application to a wide range of real-world scientific and engineering problems.

Optical soliton solutions for the Chavy-Waddy-Kolokolnikov model for bacterial colonies using two improved methods

Optical soliton solutions for the Chavy-Waddy-Kolokolnikov model for bacterial colonies using two improved methods

Solitary waves of M-fractional low-pass nonlinear electrical transmission line model arising in network system

In this study, we analyze the solitary wave behavior of a truncated M-fractional low-pass nonlinear electrical transmission line (NLETLs) model. NLETL models are relevant to computer network systems, particularly for high-speed data transmissions. They influence the behavior of signals traveling through network cables. To investigate the dynamics of solitary waves in the model, we applied the modified Sardar sub-equation and extended the sinh-Gordon equation expansion methods. We illustrated the 2D, 3D, and contour shapes of selected solutions for appropriate values of the NLETLs dynamics using Mathematica-14. Kink, anti-kink, bright-dark bell, dark bell, M-shaped periodic soliton, and logarithmic wave solutions were obtained. The results indicate that the proposed techniques may provide valuable, powerful, and efficient insights into the dynamics of nonlinear evolution models. The role of the fractional order derivative in making optical solutions is investigated in detail, which opens up opportunities for the creation of more complex models that can more accurately simulate optical phenomena in the real world.

A view of optical soliton solution of the coupled Schrödinger equation with a different approach

The goal of this study is to investigate to optical soliton solution of the nonlinear coupled space-time Schrödinger equation using the Beta derivative and Sine-Gordon Expansion Method. All calculations in this study are made using some software program and the solutions obtained are substituted in the equations. New soliton solutions have been found using the suggested method for solving these problems. The solutions obtained have important areas of use in the fields of mathematical physics, in the field of quantum physics, optic and engineering.

Dynamics of fractional optical solitary waves to the cubic–quintic coupled nonlinear Helmholtz equation

This work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects. The evolution of broad multicomponent self-trapping beams in Kerr-type nonlinear media is described by the coupled Helmholtz equation, which also take into account spatial dispersion due to non-paraxial effects. This phenomena is particularly relevant to the progressive miniaturization of optics, where the optical wavelength is similar to the beam width. It is essential to integrate non-Kerr terms, such as the self-steepening and the self frequency shift, into the coupled Helmholtz system in order to investigate the propagation of ultrashort optical pulses in the non-paraxial domain. For optical wave solutions, nonlinear ordinary equation of the governing model is achieved by applying the fractional transformation. The different types of the solutions like bright, dark, singular and mixed type solitons are extracted by applying advanced integration methods, namely modified Sardar subequation method and new Kudryashov method. These solutions provide very useful information on how the system operates. The applied approaches are highly efficient and have significant computational capability to efficiently tackle the nonlinear systems. Additionally, we include a diverse array of graphs to demonstrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. In the context of the proposed model, these visualizations assist with a comprehensive understanding of the solution’s behavior and characteristics. It is anticipated that these solutions may be significant in the study of wave propagation and related fields.