Soliton Transmission Research Articles

Predicting the dynamic behavior of soliton transmission in two ultra-short optical pulses based on improved physics-informed neural network

In this manuscript, we construct physics-informed neural network and improved physics-informed neural network by modifying the loss function, for predicting the dynamic behaviors of bright-bright single-peak solitons, bright-bright double-peak solitons and dark-bright single-peak solitons for the coupled Sasa-Satsuma equations, which depict the characteristics of two ultra-short pulses with the third-order dispersion, stimulated Raman scattering effects and self-steepening propagating simultaneously in birefringent or dual-mode fibers. Firstly, the physics-informed neural network, which is a standard model for managing the soliton prediction, is improved to a double-layer structure, to forecast the bright-bright single-peak solitons. When predicting the bright-bright double-peak solitons and dark-bright single-peak solitons, we find that the above model does not learn the dynamics of solitons, so we add the end-time conditions as the constraints according to the motion characteristics of dynamic solitions. At the same time, considering the complex boundary conditions of the dark solitons, we modify the boundary conditions in the loss function of improved physics-informed neural network for predicting bright-dark solitons. By capturing instantaneous plots at three different times and comparing the predicted values with the exact solutions, it shows that the improved physics-informed neural network is effective. Furthermore, we select the appropriate number of iterations according to the comparison of training error and training time to improve the accuracy of the model.

Interactions among lump optical solitons for coupled nonlinear Schrödinger equation with variable coefficient via bilinear method

In this paper, a non-autonomous (3+1) dimensional coupled nonlinear Schrödinger equation (NLSE) with variable coefficients in optical fiber communication is analyzed. By means of bilinear technique and symbolic computations, new multi-soliton solutions of the coupled model in different trigonometric and lump functions are given. Then, in terms of perturbed waves, considering the steady state solution and the small perturbation on the three directions x, y, z and the time t, the soliton transmission are also considered. The behaviour of interaction among lump periodic soliton is studied and optical soliton solutions are reached. This study has certain significance for the analysis of other nonlinear dispersion systems and the application of optical physics. The results are presented through graphs generated by using Maple. The important feature of the proposed study is to show different behaviour of the soliton at each component. The behaviour of solitons, their interactions, and their transformations are all governed by the fundamental concept of energy conservation in all three examples. We demonstrate the efficiency of our suggested methodology for analyzing the NLSE equations using the numerical simulations and analytical tools, yielding fresh insights into their behaviour and solutions. Our findings help to develop mathematical tools for investigating nonlinear partial differential equation (NLPDEs) and provide new insights on the dynamics of NLSE equations, which have implications for many domains of physics and applied mathematics

Stability analysis and soliton solutions of the (1+1)-dimensional nonlinear chiral Schrödinger equation in nuclear physics

The nonlinear Schrödinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton. The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems. The (1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical techniques. This work has applications in particle physics, ionised science, nuclear physics, optics, and other applied mathematical sciences. We are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures, periodic soliton solutions, chiral soliton solutions, and bell-shaped soliton solutions with the use of applied techniques. Moreover, in order to verify the scientific calculations, the stability analysis for the observed solutions of the governing model is taken into consideration. In addition, the 3-dimensional, contour, and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions. The employed strategies are dependable, uncomplicated, and effective; yet have not been utilised with the governing model in the literature that is now accessible. The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios. The methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

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.

Transmission of soliton for a coupled Radhakrishnan–Kundu–Lakshmanan equation in an optical fiber using the Jacobi elliptical sn function method

We examine a coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) equation that includes self-phase modulation, third order dispersion, self-steepening, and cross-phase modulation effects. A propagating ultrafast pulse in nonlinear systems is described by the given equation. Utilizing the coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) model, we explored the dynamics of various innovative optical solitons, such as wing-shaped, W-shaped, and brilliant solitons. We used mathematical methods like the Jacobi elliptical sn function method to get the exact analytical solution. Our results demonstrate that the self-phase modulation (SPM), self-steepening (SS), cross-phase modulation (XPM), and third order dispersion (TOD) can be effectively varied to influence the structure of the solitons. It is demonstrated that the precise balance between the self-steepening effect, the self-phase modulation, and the group velocity dispersion forms these novel W-shaped chirp-free dark solitons and dark and bright solitonic structures. By choosing appropriate settings for the physical variables, it is possible to create a graphic representation of the properties of optical solitons. The study and application of nonlinear materials with third order dispersion, cross-phase modulation, self-phase modulation effect, and self-steepening nonlinearity may take new paths as a result of our findings.

Modulation instability and collision dynamics of solitons in birefringence optical fibers

In this paper, we investigate soliton modulation instability and collision dynamics in the birefringence optical fibers. Soliton transmission in the picosecond or femtosecond range in optical fibers is described by the coupled hybrid nonlinear Schrödinger equations. We focus on the modulation instability of the plane wave solutions and the gain spectrum under different parameters. The three-soliton solutions are used to analyze soliton collisions, and the asymptotic analysis is provided to reveal the properties of soliton collisions. The elastic and inelastic collisions of three-soliton are presented, and there exists the possibility of shape restoration of one or two solitons during the three-soliton inelastic collisions. The relevant results provide not only a new perspective for the realization of optical logic gates, but also theoretical value for the experimental observation of soliton collisions.

Atomic soliton transmission and induced collapse in scattering from a narrow barrier

We report systematic numerical simulations of the collision of a bright matter-wave soliton made of Bose-condensed alkali-metal atoms through a narrow potential barrier by using the three-dimensional Gross–Pitaevskii equation. In this way, we determine how the transmission coefficient depends on the soliton impact velocity and the barrier height. Quite remarkably, we also obtain the regions of parameters where there is the collapse of the bright soliton induced by the collision. We compare these three-dimensional results with the ones obtained by three different one-dimensional nonlinear Schrödinger equations. We find that a specifically modified nonpolynomial Schrödinger equation is able to accurately assess the transmission coefficient even in a region in which the usual nonpolynomial Schrödinger equation collapses. In particular, this simplified but very effective one-dimensional model takes into account the transverse width dynamics of the soliton with an ordinary differential equation coupled to the partial differential equation of the axial wave function of the Bose–Einstein condensate.

Impact of Intense Modulation on Soliton Power Propagation across Optical Fiber and Optical Wireless Channels

The optical pulse generator model in Optisystem 20 is utilized to generate an optical soliton pulse. The performance evaluation of highly modulated soliton power transmission is carried out on both optical fiber and optical wireless communication channels. The evaluation considers a flow rate of 40 Gbps and a link distance, which is not specified in the provided context. Among the proposed modulation schemes, which include CPFSK, FSK, and PSK, CPFSK demonstrates superior performance for both communication channels. Increasing the number of bits per symbol enhances the bit error rate (BER) at the fiber or wireless channel, as received by the optical receiver, for different modulation schemes, except for the CPFSK scheme. Thus, it is evident that the CPFSK modulation scheme is more efficient and outperforms other modulation schemes for various communication channels. Hence, it is evident that the CPFSK modulation scheme exhibits superior efficiency and outperforms other modulation schemes for a variety of communication channels.

Transmission of fast solitons for the NLS with an external potential

Transmission of fast solitons for the NLS with an external potential

New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities

<p>We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. These results realize the stability of the nonlinear waves' propagation in a high-nonlinear-dispersion medium that is illustrated using 2D and 3D visuals and contour graphical diagrams of the output solutions. This research focused on determining exact soliton solutions under certain parameter conditions and evaluating the stability and reliability of the soliton solutions based on the used modified extended direct algebraic method. This will be useful for many various domains in technology and physics, such as biology, optics, and plasma physical science. At the end, we use modulation instability analysis to assess the stability of the wave solutions obtained.</p>

Transmission and control of band gap vortex solitons in fractional-order diffraction honeycomb lattices

In this paper, the existence and transmission characteristics of gap vortex optical solitons in a honeycomb lattice are investigated based on the fractional nonlinear Schrödinger equation. Firstly, the band-gap structure of honeycomb lattice is obtained by the plane wave expansion method. Then the gap vortex soliton modes and their transmission properties in the fractional nonlinear Schrödinger equation with the honeycomb lattice potential are investigated by the modified squared-operator method, the split-step Fourier method and the Fourier collocation method, respectively. The results show that the transmission of gap vortex solitons is influenced by the <inline-formula><tex-math id="M3">\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.png"/></alternatives></inline-formula> index and the propagation constant. The stable transmission region of gap vortex soliton can be obtained through power graphs. In the stable region, the gap vortex soliton can transmit stably without being disturbed. However, in the unstable region, the gap vortex soliton will gradually lose ring structure and evolves into a fundamental soliton with the transmission distance increasing. And the larger the <inline-formula><tex-math id="M4">\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.png"/></alternatives></inline-formula> index, the longer the stable transmission distance and the lower the power of the bandgap vortex soliton. When multiple vortex solitons transmit in the lattice, the interaction between them is influenced by the lattice position and phase. Two vortex solitons that are in phase and located at adjacent lattices, are superimposed with sidelobe energy, while two vortex solitonsthat are out of phase are cancelled with sidelobe energy. These vortex solitons will gradually lose ring structure and evolve into dipole modes in the transmission process. And they are periodic rotation under the azimuth angle modulating. When two vortex solitons located at non-adjacent lattice, vortex solitons can maintain a ring-shaped structure due to the small influence of sidelobes. When three gap vortex solitons are located at non-adjacent lattices, the solitons can also maintain their ring-like structures. However, when there are more than three gap vortex solitons, the intensity distribution of vortex solitons are uneven due to the sidelobe energy superimposed. These vortex solitons will form dipole modes and rotate under the azimuthal angle modulating in the transmission process. These results can offer theoretical guidance for transmitting and controlling the gap vortex solitons in the lattice.

Pre-distortion of Soliton Collision in Dual-polarization Interaction-tolerant Soliton Transmission

Pre-distortion of Soliton Collision in Dual-polarization Interaction-tolerant Soliton Transmission

A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation

In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem.

Three-Wave Mixing of Dipole Solitons in One-Dimensional Quasi-Phase-Matched Nonlinear Crystals

A quasi-phase-matched technique is introduced for soliton transmission in a quadratic [χ (2)] nonlinear crystal to realize the stable transmission of dipole solitons in a one-dimensional space under three-wave mixing. We report four types of solitons as dipole solitons with distances between their bimodal peaks that can be laid out in different stripes. We study three cases of these solitons: spaced three stripes apart, one stripe apart, and confined to the same stripe. For the case of three stripes apart, all four types have stable results, but for the case of one stripe apart, stable solutions can only be found at ω 1 = ω 2, and for the condition of dipole solitons confined to one stripe, stable solutions exist only for Type1 and Type3 at ω 1=ω 2. The stability of the soliton solution is solved and verified using the imaginary time propagation method and real-time transfer propagation, and soliton solutions are shown to exist in the multistability case. In addition, the relations of the transportation characteristics of the dipole soliton and the modulation parameters are numerically investigated. Finally, possible approaches for the experimental realization of the solitons are outlined.

Multi-peak solitons in parity-time symmetry composite Mathieu lattices

This paper numerically investigates the existence, stability, and transmission characteristics of multi-peak solitons in parity-time (PT) symmetric composite Mathieu lattices in self-focusing Kerr nonlinear media. These multi-peak solitons are highly sensitive to the incident light power, position, and phase. Different incident lights generate solitons with different transmission characteristics, especially the generation of breather soliton transmission characteristics. These findings have significant theoretical and practical implications for the fields of photonics and nonlinear optics.

High efficiency coupling fibers with different types of photo detectors for the management of noise multiplication and efficient bandwidth

Abstract This work has clarified the high efficiency coupling fibers with different types of photo detectors for the management of noise multiplication and efficient bandwidth. As well as the study of the base band signal to noise base band form ratios are clarified with EDFA base band amplifier length variations. Max Q form factor with EDFA amplifier base band length variations is also demonstrated. The optimum base band electrical signal form power is simulated with EDFA base band amplifier length variations. The simulative study of Ge and InGaAs PIN photo-detectors performance evaluation are studied in the presence of the soliton transmission fiber systems. The dispersion management by the soliton technique to reach the value around zero. The max base band signal power form is clarified versus time based Ge and InGaAs PIN photo-detectors. Total base band electrical power form based Ge and InGaAs PIN photo-detectors are demonstrated. Max signal base form power amplitude band is simulated with the spectral base band frequency based Ge and InGaAs PIN photo-detectors. The max signal base form power amplitude band is studied versus time based Ge PIN photo-detectors.

Optical soliton perturbation of the quintic Gerdjikov-Ivanov model

This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which models optical soliton transmission in the photonic crystal fibers and optical fibers. With the aid of the new Kudryashov scheme, we successful achieved the bright and dark solitons and we simulated their graphical presentation.

Data-driven prediction of spatial optical solitons in fractional diffraction

A quasi-residual physics-informed neural network (QR_PINN) with efficient residual-like blocks, was investigated based on classical physics-informed neural network to solve nonlinear fractional Schrödinger equation and analyze the transmission of spatial optical solitons in saturable nonlinear media with fractional diffraction. A comprehensive verification of stable transmission of various solitons under PT-symmetric potential was carried out using the QR_PINN. In addition, the transmission of spatial optical solitons was studied under simple real potential (stable transmission) and complex Scarf-II potential (unstable transmission). The results show that the QR_PINN can accurately reconstruct the transmission of spatial optical solitons under fractional diffraction. Meanwhile, as the complexity of the potential function increases, the prediction accuracy of the QR_PINN slightly decreases. These results provide a new approach for the application of deep learning in the nonlinear fractional Schrödinger equation.

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers, a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed. In this paper, in order to study the dynamic mechanism of femtosecond solitons in different media, we take the nonlinear Schrödinger equation considering higher-order effects as the theoretical model, discuss the propagation of solitons in single-mode fibers, and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons. The exact solution of the theoretical model is obtained through the bilinear method, and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied. The influence of various conditions on the transmission and interaction of optical solitons is explored. Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested. The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Optical solitons of (2+1)-dimensional Biswas–Milovic model with Kerr and parabolic laws of self-phase modulation

In this work, we consider the (2+1)-dimensional Biswas–Milovic equation, which was recently formed. The (1+1)-Biswas–Milovic equation which is a special case of the Schrödinger’s equation and it was introduced in 1910. Although there have been many studies on the (1+1) form of the equation, there are hardly any studies on the recently adopted (2+1) and (3+1) forms. Most of the time, it is more meaningful to interpret physical phenomena such as physics, ocean waves, genetics, earthquake, optics depending on the (2+1) and (3+1) dimensional models. Depending on the effect and importance of different nonlinearities forms of self-phase modulation on soliton transmission, obtaining optical soliton solutions under the Kerr and parabolic-law nonlinearities forms of the (2+1)-dimensional Biswas–Milovic equation has been investigated by the new Kudryashov scheme, which was introduced to the literature by N. A. Kudryashov recently. Converting the examined nonlinear partial differential equation to nonlinear ordinary differential form with complex wave transform, obtaining the linear algebraic system by applying the considered method on the transformed form, deriving optical soliton solutions from this system by determining the unknown parameters of the model and method, are the methodologies that form the main framework of the article. Bright, W-like and singular solitons of the analyzed problem were obtained, graphical presentations were made and necessary explanations were made in the relevant sections. The change of the bright soliton to a W-like appearance as an effect of the parabolic law nonlinearity parameter is one of the points obtained and also emphasized in the study.