Propagation Of Optical Solitons Research Articles

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

Abstract When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schrödinger equation, we analytically explore the evolution of optical solitons in the presence of high-order nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.

M-truncated fractional form of the perturbed Chen–Lee–Liu equation: optical solitons, bifurcation, sensitivity analysis, and chaotic behaviors

This investigation discusses the modified M-truncated form of the perturbed Chen–Lee–Liu (pCLL) dynamical equation. The pCLL equation is a generalization of the original CLL equation, which describes the propagation of optical solitons in optical fibers. The pCLL equation includes additional terms that account for various influences such as chromatic dispersion, nonlinear dispersion, inter-modal dispersion, and self-steepening. A new version of the generalized exponential rational function method is utilized to obtain multifarious types of soliton solutions. Moreover, the planar dynamical system of the concerned equation is created using a Hamiltonian transformation, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are added to the analytical results to better understand the dynamic behavior of these solutions. The study’s findings could be extremely useful in solving additional nonlinear partial differential equations.

Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

This research explores the dual-mode manifestation within the nonlinear Schrödinger equation, elucidating the amplification or absorption of paired waves. This study delves into the simultaneous generation of two distinct waves associated with the dual-mode phenomenon with three crucial parameters: phase velocity, nonlinearity and dispersive factor. The resulting wave phenomena from these solutions have implications across various fields, including fluid dynamics, water wave mechanics, ocean engineering and scientific inquiry. The study employs the modified Sardar sub-equation method to obtain the optical soliton solutions, encompassing various types such as dark, bright, singular, combo dark–singular, periodic singular and dark–bright solitons. The obtained results highlight the reliability and simplicity of the modified Sardar sub-equation method. Additionally, the paper delves into the parametric conditions crucial for shaping and sustaining these solitons. The research explores the interaction of dual waves and the variation in wave speed. Furthermore, dynamic phenomena are illustrated, and the physical implications of the solutions are interpreted using 3D and 2D plots with different parameter values.

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

Extraction of optical wave structures to the coupled fractional system in magneto-optic waveguides

In this article, truncated M-fractional coupled nonlinear Schrodinger equation (NLSE) with quadratic–cubic nonlinearity is under observation. The studied model is composed of chromatic dispersion, magneto-optic parameter and inter-modal dispersion. The NLSE is the most significant physical model to explain the fluctuations of optical soliton proliferation. The NLSEs have become more popular because of the clarity with which they explain a wide range of complex physical phenomena and the depth with which they display dynamical patterns via localized wave solutions. Optical soliton propagation in magneto-optic is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. The optical solitons are secured in the forms of bright, dark, singular and combo solitons. In addition, hyperbolic, periodic and exponential function solutions have been recovered. The modified Sardar subequation and enhanced modified extended tanh-expansion approaches recently developed integration tools are adopted in this study for securing the solutions. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The effect of parameters have been observed by allotting suitable values and sketching the different shapes of the graphs.

Analyzing optical soliton propagation in perturbed nonlinear Schrödinger equation: A multi-technique study

In this study, the extended hyperbolic function method and unified solver method are applied to examine the propagation of optical solitons in perturbed nonlinear Schrodinger equation. The proposed techniques are characterized as simpler, more concise, and straightforward. They allow for the extension of the class of solutions and the retrieval of a diverse range of optical solitons, including singular, periodic singular, bright, and dark ones. This highlights the significance of the results. The authors emphasize the novelty of these techniques, as they have not been previously applied to recover optical solitons in this model These out comes may be beneficial for further understanding of numerous phenomena that arises in various physical systems and can be castoff for the optical communication resolution. The existence measures for these solutions are also unveiled in the form of constraint parameters. In addition, the pictorial representations of certain solutions depicted in figures undoubtedly play a key role in understanding the behavior and apprehending some of the physical features of the the discovery of a plethora of novel soliton solutions and their accompanying behaviors.

Sensitivity analysis and propagation of optical solitons in dual-core fiber optics

Sensitivity analysis and propagation of optical solitons in dual-core fiber optics

DYNAMICS OF OPTICAL WAVE PROFILES TO THE FRACTIONAL THREE-COMPONENT COUPLED NONLINEAR SCHRÖDINGER EQUATION

This paper explores the truncated [Formula: see text]-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

EXACT TRAVELING WAVE SOLUTIONS OF THE COUPLED LOCAL FRACTIONAL NONLINEAR SCHRÖDINGER EQUATIONS FOR OPTICAL SOLITONS ON CANTOR SETS

Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission.

Optical soliton for (2+1)-dimensional coupled integrable NLSE using Sardar-subequation method

The [Formula: see text]-dimensional coupled nonlinear Schrödinger equation has versatile applications for modeling nonlinear waves in different areas such as optics, atmospheric science, fluid dynamics, and plasma physics. This study focuses on the propagation of optical solitons and their interaction within various mediums such as multi-mode fiber and fiber arrays. The Sardar-subequation method is applied to achieve the bright, dark, combined bright–dark, periodic, combined dark-singular and singular optical solitons solutions. The 3D, contour and 2D profiles for some of the assimilation solutions are also plotted to show the physical behavior of the solutions. The obtained results demonstrate the effectiveness of the adopted methodology in obtaining traveling wave solutions and have many applications in applied mathematics and engineering. The novelty of our work lies in the successful application of Sardar-subequation method in obtaining diverse soliton solutions and exploring their physical behavior. This study goes beyond previous efforts in the literature by presenting a comprehensive analysis of soliton dynamics. This ability to describe and predict the behavior of optical solitons in diverse mediums opens up new opportunities for investigating the existing systems.

Optical soliton solution via complete discrimination system approach along with bifurcation and sensitivity analyses for the Gerjikov-Ivanov equation

The aim of this research intends to investigate the complex wave patterns and dynamic behavior of the Gerjikov-Ivanov equation (GIE), commonly known as the derivative nonlinear Schrödinger equation (DNLSE). The GIE model is the one that examines dynamics of optical soliton propagation for transmission technologies, including transcontinental and transoceanic lengths of optical fibers, data transfer, and the telecommunications sector. The GIE equation can be regarded as an extension of the NLSE when certain higher-order nonlinear effects are taken into account. We study various optical soliton solutions, including Jacobian elliptic, hyperbolic, and trigonometric functions, are identified using the polynomial method’s complete discrimination system (CDSPM). In addition, Jacobian elliptic functions can be transformed into solitary wave solutions. We also discuss bifurcation points, sensitivity analysis and critical solution conditions, offering a thorough grasp of the system’s dynamic features. The CDSPM plays an important role in studying equilibrium points, phase diagrams, bifurcation behavior, and performing quantitative and qualitative evaluations.

On soliton solutions for higher-order nonlinear Schrödinger equation with cubic-quintic-septic law

The topic of dispersive optical solitons is one of the essential areas of telecommunications engineering. This paper presents the nonlinear Schrödinger equation (NLSE) with the cubic-quintic-septic (CQS) law which includes higher-order dispersion terms. This equation examines the dynamics of dispersive optical solitons propagation in nonlinear optical fibers. The presented model is significant in mathematics and theoretical physics sciences because long-distance optical fibers are used in optical communication utilized for transoceanic and intercontinental data transmission. First, the considered equation is transformed into a nonlinear ordinary differential equation (NLODE) using the traveling wave transformation. Then, two powerful techniques, Sinh-Gordon expansion approach and the auxiliary equation method (AEM), based on the homogeneous balance rule, are operated to produce analytical solutions for the NLSE with CQS law. Thus, bright, dark, singular, and periodic-singular soliton solutions are acquired. We demonstrate the three-dimensional (3D) and two-dimensional (2D) representations to interpret the physical behavior of some derived solutions. Besides, we investigate the effects of some parameters in the model with graphical illustrations. Therefore, it can be noted that the obtained soliton solutions have a significant role in soliton dynamics.

Polar compactons and solitons in a two dimensional optical waveguide: Theory and simulations

The propagation of optical cylindrical compactons and solitons in a two dimensional nonlocal nonlinear waveguide is deeply investigated by carrying a particular emphasis on its nonlinear response function. Considering the weakly nonlocal medium, the two dimensional nonlocal nonlinear Schrödinger equation describing the propagation of signal light is derived. This equation contains the basic nonlinear Schrödinger equation with additional nonlinear terms proportional to the second order space derivative of coordinates in the transverse directions. By seeking the solution in polar form, this equation is separated into real and imaginary parts, followed by the analysis of the equilibrium points and their stability, predicting the type of solutions. These solutions are found both with linear and nonlinear phases through direct integration. In order to seek polar solutions, the nonlocal nonlinear Schrödinger equation is expressed in cylindrical coordinate and the resulting equation, containing additional terms inversely proportional to the radius r is not easily solvable. The type of solutions of this equation is predicted by the investigation of new equilibrium points and their stability. The analytical cylindrical compactons and pulse solitons as solutions of this equation are provided by using the Rayleigh–Ritz variational method, usually used for symmetric radial solitons to approximate pulse solitons in polar coordinate, and the stability of these solutions is checked through numerical investigations.

Extraction of solitons in magneto–optic waveguides for coupled NLSEs with Kudryashov's law of nonlinearity via modified extended direct algebraic method

In this paper, the modified extended direct algebraic technique is used for determining new and various traveling wave solutions to the coupled nonlinear Schrödinger equation (NLSE) with Kudryashov's law of nonlinearity. This model describes the propagation of optical solitons through magneto-optic wave-guides. Various solutions such as dark solitons, singular solitons, hyperbolic solutions, singular periodic solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic function solution are raised. To demonstrate the physical behavior of the obtained solutions, 3D and 2D graphs are introduced.

Some new wave solutions and modulation instability of a Hamiltonian amplitude equation in optical fibres

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term Lxt is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp(−ξ(δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model.

Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair

Under consideration in this study is the discrete coupled modified Korteweg–de Vries (mKdV) equation with 4 × 4 Lax pair. Firstly, through using continuous limit technique, this discrete equation can be mapped to the coupled KdV and mKdV equations, which may depict the development of shallow water waves, the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma. Secondly, the discrete generalized (r, N–r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem, from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background, higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived, and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique. Finally, the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions. These results may be helpful for understanding some physical phenomena in fields of shallow water wave, optics, and plasma physics.

Qualitative analysis of stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity

In this paper, the stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity is studied, which is usually used to describe the mathematical model of optical soliton propagation in dispersive optical fibers from the field of nonlinear optics. Firstly, the stochastic Schrödinger–Hirota equation is converted into two-dimensional planar dynamic system by using the traveling wave transformation. Secondly, the qualitative analysis of the stochastic Schrödinger–Hirota equation is discussed by using the theory of planar dynamical systems. Finally, the chaos pattern of the stochastic Schrödinger–Hirota equation with perturbed system is considered. What is more, phase portraits and sensitivity analysis of the perturbed system are plotted by using the Maple software.

Optical soliton propagation in the Benjamin–Bona–Mahoney–Peregrine equation using two analytical schemes

The purpose of this research is to investigate the nonlinear partial differential equation known as Benjamin–Bona–Mahoney–Peregrine equation. Two versatile techniques, namely the extended (G′G2)-expansion method and modified auxiliary equation method is used to extract the exact solutions of the nonlinear Benjamin–Bona–Mahoney–Peregrine equation. Consequently, a diverse range of novel collections of exact traveling wave solutions are identified such as kink, bright, singular kink and periodic soliton solution. To provide a physical understanding, several of the discovered solutions are shown in figures. The resulting solutions are of the trigonometric, hyperbolic, and rational varieties and the stability analysis are also discussed. In addition to this, the graphical aspects of the produced solutions are investigated. Due to the vital necessity of this aspect, we make use of the suitable parameter values to place a priority on the physical aspects of the provided findings by utilizing 3D and contour charts. The suggested procedures are of great use and can be extended to additional nonlinear evolutionary equations that reflect nonlinear physical frameworks in the nonlinear sciences.

Optical solitons in curved spacetime

Light propagation in curved spacetime is at the basis of some of the most stringent tests of Einstein’s general relativity. At the same time, light propagation in media is at the basis of several communication systems. Given the ubiquity of the gravitational field, and the exquisite level of sensitivity of optical measurements, the time is ripe for investigations combining these two aspects and studying light propagation in media located in curved spacetime. In this work, we focus on the effect of a weak gravitational field on the propagation of optical solitons in non-linear optical media. We derive a non-linear Schrödinger equation describing the propagation of an optical pulse in an effective, gradient-index medium in flat spacetime, encoding both the material properties and curved spacetime effects. In analyzing the special case of propagation in a 1D optical fiber, we also include the effect of mechanical deformations and show it to be the dominant effect for a fiber oriented in the radial direction in Schwarzschild spacetime.

Ultrafast Long-Distance Electron-Hole Plasma Expansion in GaAs Mediated by Stimulated Emission and Reabsorption of Photons.

Electron-hole plasma expansion with velocities exceeding c/50 and lasting over 10ps at 300K was evidenced by time-resolved terahertz spectroscopy. This regime, in which the carriers are driven over >30 μm is governed by stimulated emission due to low-energy electron-hole pair recombination and reabsorption of the emitted photons outside the plasma volume. At low temperatures a speed of c/10 was observed in the regime where the excitation pulse spectrally overlaps with emitted photons, leading to strong coherent light-matter interaction and optical soliton propagation effects.