Optical Solutions Research Articles

Multicomponent nonlinear fractional Schrödinger equation: On the study of optical wave propagation in the fiber optics

In this article, we investigate the soliton wave dynamics of the fractional three-component coupled nonlinear Schrödinger equation. This equation is considered as a fundamental tool for describing the behavior of optical pulses in optical fibers. There is increasing interest in studying these equations as they can be used to explain a wide range of complex physical phenomena in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. In order to obtain the required solutions, the first step is to apply the complex wave transformations with β-fractional derivative to obtain the nonlinear ordinary differential equations of the governing model. Furthermore, by applying the novel integration methods known as generalized Arnous method and multivariate generalized exponential rational integral function approach, different type of soliton solutions are extracted. Different sets and values of the physical parameters are used to study the optical soliton solutions of the studied system. Based on a comparative analysis of our results with existing techniques, this study concludes that our proposed solutions are novel. The results described in this work are able to enhance the nonlinear dynamical behavior of a given system and confirm the effectiveness of the methods used. Furthermore, the different graphs are sketched to visualize the solutions behavior with various parametric values. It is anticipated that obtained solutions will be significant in the study of wave propagation and other related fields.

Stability, modulation instability and traveling wave solutions of (3+1)dimensional Schrödinger model in physics

The nonlinear Schrödinger equation is one of the most important physical model in optical fiber theory for comprehension of the fluctuations of optical bullet development. In this study, the exact bullet solutions for the (3+1)-dimensional Schrödinger equation which demonstrate the bullet behaviours in optical fibers can be accumulated through the Sardar sub-equation method and the unified method. The applied strategies may retrieve several kinds of optical bullet solutions within one frameworks as well as is quite simple and reliable. Mathematica are utilised for describing the dynamics of different wave structures as 3D, 2D, and contour visualisations for a given set of parameters. As a result, we are able to develop a variety of travelling wave structures namely the periodic, singular and V shaped soliton wave solutions. The stability analysis for the derived results is analysed efficiently while the modulation instability for the governing model has also been studied to demonstrate the reliability of the research. The approaches implemented here works perfectly and can be extended to deal with many advanced models in contemporary areas of science and engineering. The solutions attain by using these techniques are robust, unique and straight forward and has applications in different fields of physics, engineering and mathematical science. Specially physical applications of these obtain results are in the transmission of data in optical fibers. We also add the graphics for the better understanding of the attain solutions behaviour.

Exploration of solitary waves and periodic optical soliton solutions to the nonlinear two dimensional Zakharov–Kuzetsov equation

Exploration of solitary waves and periodic optical soliton solutions to the nonlinear two dimensional Zakharov–Kuzetsov equation

Dynamical optical soliton solutions and behavior for the nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index together with the dual-form of nonlocal nonlinearity

Dynamical optical soliton solutions and behavior for the nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index together with the dual-form of nonlocal nonlinearity

Exploration of Soliton Solutions in Nonlinear Optics for the Third Order Klein-Fock-Gordon Equation and Nonlinear Maccari’s System

Exploration of Soliton Solutions in Nonlinear Optics for the Third Order Klein-Fock-Gordon Equation and Nonlinear Maccari’s System

Lie symmetry analysis of cubic–quartic optical solitons having cubic–quintic–septic–nonic form of self-phase modulation structure

AbstractThe present study examines optical solitons characterized by cubic–quartic dynamics and featuring a self-phase modulation structure encompassing cubic, quintic, septal, and nonic terms. Soliton solutions are obtained through Lie symmetry analysis, followed by integration of the resulting ordinary differential equations using Kudryashov’s auxiliary equation method and a hyperbolic function approach. A comprehensive range of optical soliton solutions has been recovered, alongside the revelation of their criteria for existence.

Advanced optical transceiver and switching solutions for next-generation optical networks

Innovative transceiver and switching approaches should be explored with special focus on flexibility, energy efficiency, sustainability, and interoperability to be adopted on next-generation 6G optical networks driven by the diverse landscape of emerging applications and services and increasing traffic demand. In this regard, multiband (MB) and spatial division multiplexing (SDM) technologies arise as promising technologies for providing suitable network capacity scaling while fulfilling the stringent requirements of the incoming 6G era. In this paper, innovative MB over SDM (MBoSDM) switching node and sliceable bandwidth/bit rate variable transceiver (S-BVT) architectures with enhanced capabilities and features are proposed and experimentally validated. Different network scenarios have been identified and assessed, enabling up to 180.9 Gb/s S+C+L transmission in back-to-back (B2B) configuration. A MBoSDM scenario including both transceiver and switching solutions is demonstrated, including a 19-core multi-core fiber (MCF) of 25.4 km. Thanks to the transceiver modular and scalable approach, higher capacities can be envisioned by enabling multiple slices working in the different bands beyond the C-band. A power efficiency analysis of the proposed transceiver is also presented, including a pathway towards the integration with a software defined networking (SDN) control plane assisted by energy-aware artificial intelligence (AI)/machine learning (ML) trained models.

Optical soliton solutions in optical metamaterials with full nonlinearity

Optical soliton solutions in optical metamaterials with full nonlinearity

Optical solitary waves solutions of the eight-order dispersive Schrödinger wave equation

Optical solitary waves solutions of the eight-order dispersive Schrödinger wave equation

Quantum Brain Dynamics: Optical and Acoustic Super-Radiance via a Microtubule

We aim to derive a super-radiance solution of coherent light and sound waves involving water degrees of freedom in the environment of a microtubule. We introduce a Lagrangian density functional of quantum electrodynamics with non-relativistic charged bosons as a model of quantum brain dynamics (QBD) involving water molecular conformational states and photon fields. We also introduce the model of charged boson fields (water degrees of freedom) coupled with phonons. Both optical and acoustic super-radiance solutions are derived in our approach. An acoustic super-radiance mechanism involving information transfer is proposed as an additional candidate to solve the binding problem and to achieve acoustic holography. Our results can be applied to achieve holographic memory storage and information processing in QBD.

Challenges for Multiband Optical Amplification and Solutions Therefore

Challenges for Multiband Optical Amplification and Solutions Therefore

Chaotic behavior, bifurcations, sensitivity analysis, and novel optical soliton solutions to the Hamiltonian amplitude equation in optical physics

This study, highlights the exact optical soliton solutions in the context of optical physics, centering on the intricate Hamiltonian amplitude equation with bifurcation and sensitivity analysis. This equation is pivotal in optics which underpins the understanding of optical manifestations, encompassing solitons, nonlinear consequences, and wave interactions. Applying an analytical expansion approach, we extract diverse optical solutions, having trigonometric, hyperbolic, and rational functions. Next, we utilize concepts from the principle of planar dynamical systems to investigate the bifurcation processes and chaotic behaviors present in this derived system. Additionally, we use the Runge–Kutta scheme to carry out a thorough sensitivity analysis of the dynamical system. It has been verified through this analytical process that small variations in beginning conditions have negligible effects on the stability of the solution using bifurcation analysis. Validation via Mathematica software ensures the accuracy of these findings. Furthermore, we employ dynamic visualizations, such as 2D, 3D, and contour plots, to illustrate various soliton patterns, including kink, multi-kink, single periodic, multi-periodic, singular, and semi-bell-shaped configurations. These visual representations provide a glimpse into the fascinating behavior of optical phenomena. The solutions obtained via this proposed method showcase its efficacy, dependability, and simplicity in comparison to various alternative approaches.

Soliton waves with optical solutions to the three-component coupled nonlinear Schrödinger equation

This study uses the modified Sardar sub-equation method to find novel soliton solutions to the nonlinear three-component coupled nonlinear Schrödinger equation (NLSE), which is used for pulse propagation in nonlinear optical fibers. Multi-component NLSE equations are widely used because they can represent a wide range of complex observable systems and more dynamic patterns of localized wave solutions. The optical solutions proposed in this study are novel and can be described using hyperbolic, trigonometric, and exponential functions. These solutions are categorized as bright, dark, singular, combo bright-singular, and periodic solutions. Some solutions’ dynamic behaviors are demonstrated by selecting appropriate physical parameter values. The results and computational analysis indicate that the techniques provided are simple, effective, and adaptable. They can be applied to a variety of nonlinear evolution equations, whether stable or unstable, and can be used in fields such as mathematics, mathematical physics, and applied sciences.

Modulation instability and extraction of fractional optical solitons in the presence of generalized Kudryashov’s law and dual form of non-local nonlinearity

This research delves into the study of optical solitons governed by Kudryashov’s law of nonlinear refractive index, incorporating a conformable fractional derivative, perturbed terms, and a quadrupled-power law in optical fibers. Employing a novel approach known as the generalized exp(− S(ζ) ) expansion method, we identify novel optical soliton solutions characterized by exponential, rational, and hyperbolic functions featuring a conformable fractional derivative. These solutions manifest as unified bright-dark, singular, singular periodic, kink, anti-kink, and novel solitary waves. We employ 3D, contour, and 2D plots to analyze the behavior of these solutions across different temporal and fractional-order derivative parameters, offering an understanding of their physical interpretations. Furthermore, we perform modulation instability (MI) analysis that depends on standard linear stability analysis to derive the MI gain spectrum, demonstrating how well our methodology works for nonlinear problems in the natural sciences and engineering domains. This approach provides an effective way to investigate optical solutions in various integer and fractional Schrödinger equations.

Correction to: Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

Correction to: Bifurcations, chaotic behavior, sensitivity analysis and new optical solitons solutions of Sasa-Satsuma equation

New optical soliton solutions to the Biswas–Milovic equations with power law and parabolic law nonlinearity using the Sardar-subequation method

New optical soliton solutions to the Biswas–Milovic equations with power law and parabolic law nonlinearity using the Sardar-subequation method

Optical Soliton solutions for stochastic Davey–Stewartson equation under the effect of noise

In this manuscript, we investigates the stochastic Davey–Stewartson equation under the influence of noise in Ito^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\hat{o}}$$\\end{document} sense. This equations is a two-dimensional integrable equations, are higher-dimensional variations of the nonlinear Schrödinger equation. Plasma physics, nonlinear optics, hydrodynamics, and other fields have made use of the solutions to the stochastic Davey–Stewartson equations. The Sardar subequation method is used that will gives us the the stochastic optical soliton solutions in the form of dark, bright, combine and periodic waves. These exact optical soliton solutions are helpful in understanding a variety of fascinating physical phenomena because of the importance of the Davey- Stewartson equations in the theory of turbulence for plasma waves or in optical fibers. Additionally, we use Mathematica tools to plot our solutions and exhibit a series of three-dimensional, two-dimensional and their corresponding contour graphs to show how the noise affects the exact solutions of the stochastic Davey–Stewartson equation. We show how the stochastic Davey–Stewartson solutions are stabilised at around zero by the multiplicative Brownian motion.

Bright optical solution for fractional Lakshmanan–Porsezian–Daniel with spatio temporal dispersion by improved Adomian decomposition method

Bright optical solution for fractional Lakshmanan–Porsezian–Daniel with spatio temporal dispersion by improved Adomian decomposition method

Optical Soliton Solutions to the Strain Wave Model with Micro-Structured Solid using Two Analytical Approaches

Optical Soliton Solutions to the Strain Wave Model with Micro-Structured Solid using Two Analytical Approaches

New optical soliton solutions to nonlinear Schrödinger equation with fractional temporal evolution having parabolic and dual power law nonlinearities

New optical soliton solutions to nonlinear Schrödinger equation with fractional temporal evolution having parabolic and dual power law nonlinearities