Search

This manuscript elaborate a novel characteristic of stochastic multi breather type, periodic, hybrid periodic and different type of waves solutions for the Shrödinger–Hirota (SH) equation. The mentioned equation is studied by a Wiener process and white noise which is used for the sudden and large-scale fluctuation. By applying the wave transformation technique the considered equation is transformed into ordinary differential equations, gives meaningful analysis. From the solution of the SH equation various type of results, including breather like waves, hybrid periodic waves, and singular solitons. Breather waves are applied in optical fiber communications, oceanography, and plasma physics. Singular waves find use in medical imaging, seismic research, and nonlinear optics. Hybrid singular-periodic waves have applications in photonics, acoustics, and material science, enabling advancements in diverse fields. To visually capture these intricate behaviors, we used Mathematica software to generate 2D and 3D graphs of the analytical stochastic solutions. This combination of mathematical rigor and numerical simulations provides a comprehensive understanding of the phenomena under study, making a valuable contribution to the field of nonlinear wave equations and stochastic processes. [ABSTRACT FROM AUTHOR]

This work simulates the (1+1)-dimensional nonlinear perturbed Schrödinger model (NLPSM ). Hydrodynamics, elastic media, nonlinear optical fiber communication, and plasma physics are just a few of this model's mathematical physics and engineering applications. The study aims to accomplish two main objectives. First, it seeks to find unique soliton solutions such as solitary, dark, periodic, and plane wave solutions that haven't been found in the literature before using the modified Sardar sub-equation approach (MSSEA ). Second, a novel approach to analysis called bifurcation analysis is used to investigate the dynamic behavior of the model. Physical compatibility findings are supported by density, 3-D, and 2-D illustrations made with parametric variables. The analysis shows that the approach used to quickly acquire complete and typical answers was successful. This approach works well for solving challenging problems in physics, engineering, mathematics and fiber optic phenomena. [ABSTRACT FROM AUTHOR]

This work focuses on the study of the paraxial wave model with a space–time fractional form. This model has more importance for describing light propagation in nonlinear optical fibers and telecommunication lines. The main aim of this work is to observe the effect of the fractional parameters and compare the truncated M -fraction with the beta-fraction, conformable fraction form, and classical form of the PW model. For this observation, we applied the Simplest equation technique to acquire analytical solutions to the space–time (spatiotemporal) M -fractional paraxial wave model. We are able to acquire several new optical soliton solutions, including periodic waves, kink-type waves, rogue-type waves, and several novel periodic waves, by providing the appropriate fractional parametric values. These solutions have significance for shedding light on a number of physical phenomena in the realms of optical fiber and communication sciences. The diverse values of fractional parameters and the three-dimensional and contour plot graphs of certain chosen solutions are depicted, which are the most accurate physical characterizations of the outcomes. We also sketch the comparative graph of diverse fractional forms and the classical form of the paraxial wave equation in two-dimensional plots. Consequently, our findings represent an important breakthrough in this complex area and help further develop our comprehension of the behavior of solitons. [ABSTRACT FROM AUTHOR]

The Quantum Noise Stream Cipher (QNSC) is offering very high security in physical layer of optical fiber communication network to meet the today's main requirement of secure networks. However, the problem of timing and carrier frequency offset synchronization was higher for Coherent optical orthogonal Frequency Division Multiplexing (CO-OFDM) systems using QNSC for network security. For higher-order modulation systems, the algorithms used to overcome this problem are offering very low accuracy. In addition to this, the chances of attack by an illegal receiver are more due to no encryption used for the preamble creation. Existing algorithms used to create a new preamble is: CNI ((conjugate, negative, and image) with Pseudo-Noise sequence) and CNC ((conjugate and negative) with Chu sequence). In this paper, ConvNN (Convolutional Neural Network) and CapNN (Capsule Neural Network) based joint synchronization of timing and frequency for CO-OFDM system is proposed. From the experiments, performed at 10Gbps, it has been illustrated that the proposed networks are giving more robust results. In addition to these proposed networks are offering better and secure performance for both timing and frequency offset synchronization by using less training data. [ABSTRACT FROM AUTHOR]

This study explores optical soliton solutions within the framework of the Caudrey–Dodd–Gibbon equation (CDGE) and the ( 1 + 1 )-dimensional Boussinesq equation, utilizing the modified Sardar sub-equation method (MSSEM). The derived solutions are meticulously verified using symbolic software Mathematica and encompass a rich array of mathematical functions, including trigonometric, hyperbolic, and exponential functions. Visualization techniques, such as 3D plots, 2D plots, density graphs, and contour graphs, effectively illustrate the diverse behaviors exhibited by these soliton solutions. These equations have been studied previously, their comprehensive traveling wave solutions are relatively unexplored. By employing the modified Sardar sub-equation method, which has demonstrated effectiveness in solving nonlinear evolution equations, this study aims to bridge this gap. The soliton solutions obtained encompass a wide spectrum of behaviors, including bright, dark, periodic, singular, dark-periodic, bright-periodic, dark-singular, compactons, and bright-singular soliton solutions, as well as other complex phenomena. The comprehensive exploration of soliton solutions not only enhances our understanding of fundamental wave phenomena but also provides valuable insights for addressing nonlinear equations across various scientific disciplines, including optical fiber communications, plasma physics, and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

The use of optical fiber for communication has grown at a rapid pace due to the demands of the modern information era. In this paper, the modified extended direct algebraic method is implemented to explore optical solitons and other exact wave solutions for the coupled system of perturbed highly dispersive complex Ginzburg–Landau equation with polynomial nonlinearity law which describe the transmission of solitons in birefringent fibers. The obtained solutions include bright solitons, dark solitons, singular solitons and combo dark-singular solitons. Additionally, Jacobi elliptic function solutions, exponential solutions, and singular periodic solutions are also offered. To ensure the existence of the obtained soliton solutions, we set some constraints on the parameters. In addition, some selected solutions are visually shown to demonstrate the physical properties of the exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, using the Hirota bilinear method, we investigate the perturbed Gerdjikov–Ivanov equation (PGIE) for lump soliton, rogue wave, periodic and kink cross rational solutions, homoclinic breathers, M-shaped and many other interactions. All these solutions have so many real life applications for example lump wave help to study the behavior of vortices and eddies in the ocean, which are used for climate modeling and fisheries management. Rogue waves are used in maritime safety, M-shaped solitons are used in optical fiber communications to transmit data over long distances without distortion, improving the efficiency and reliability of high-speed data transmission. Breathers can be used in fiber optic systems to generate ultrafast optical pulses, which have applications in telecommunications and laser technology. We also discuss the dynamical behaviour of our solutions in various dimensions. [ABSTRACT FROM AUTHOR]

The Schrödinger–Hirota equation are studied in light transmission, optical fiber communication, and nonlinear effects in optics. The auxiliary equation method is not only suitable for solving specific types of nonlinear partial differential equations, but also has strong applicability to all kinds of different types of equations. It helps us to deduce the exact solution of the equation faster and analyzes the dynamic behavior of the system further. The extended fourth Jacobi elliptic equation is used in this paper to seek different types of exact solutions, which include bright soliton solutions, kink solutions, periodic wave solutions, and singular traveling wave solutions via selecting appropriate parameters.The characteristics of some solutions are graphically presented using two- and three-dimensional graphs such as the real part, the imaginary part, and their modulus via providing suitable values to arbitrary parameters. Compared to other methods, the method is more direct and easier for calculations. Kindly check and confirm the edit made in the title. The edit made in the title is correct. The word "extended" in the title can be deleted if necessary. [ABSTRACT FROM AUTHOR]

Fiber pump lasers are widely used in a variety of fields, such as optical fiber communication, national defense, and medical beauty due to their high beam quality and intense laser energy. However, the alignment errors of optical parameters can influence the beam quality in the packaging of the fiber pump lasers. It is necessary to analyze the reflector, focusing lens, fiber, and the laser diode on the coupling influence between for guiding the fiber pump laser packaging. Firstly, we establish the optical path between the laser diode, focusing lens and reflector based on the physical ray-tracing method. On the other hand, the high coupling efficiency of whole system is achieved by optimize the parameters of each optical element. The simulation result shows that the highest coupling efficiency is 98.6% based on optimizing the parameters of the optical path while the experimental result of coupling efficiency is 90.36%. Also, the effects of refractive index, wavelength and fiber diameter on coupling efficiency are further investigated. The experimental results show that the radial displacement has the greatest influence on the coupling efficiency. The simulation results show that increasing the fiber core diameter can effectively improve the coupling efficiency. The results of rigorous analysis will provide an effective reference for manufacturing compact, high coupling efficiency fiber pumped laser. [ABSTRACT FROM AUTHOR]

Data privacy is becoming more important as the internet of things (IoT) rapidly expands. There are significant consequences for the broad adoption of the internet of things. Homomorphic encryption is one possible solution for protecting sensitive data in the IoT. However, there is a great deal of potential for efficiency gains. In order to get enough privacy and security, it is also crucial. Our homomorphic encryption technique for secure and private optical fibre communication is detailed in this publication. The data owner, fog server, and data consumers' privacy is the primary focus of the proposed architectural design. The performance of this research shows that our FCHE solution improves data security throughout the data storage operation and reduces encryption length. This research also aims to analyse the factors of optical fiber communication cost, storage cost, and computing cost in the context of FCHE. [ABSTRACT FROM AUTHOR]

This study addresses dual-mode equations, focusing on the nonlinear wave behavior characterized by simultaneous bidirectional movement influenced by a specific phase velocity. Building upon Korsunsky's enhanced Korteweg-De Vries equation, we introduce an innovative dual-mode simplified modified Camassa-Holm model and systematically analyze its solutions. Employing explicit tanh / coth , Exp-function expansion, extended Kudryashov-expansion, and rational sin / cos techniques, we establish soliton solution constraints. The validation process includes generating supportive 3D and 2D plots. Furthermore, the study is exploring the interaction between dual waves and how the speed of waves changes. The outcomes of this research are expected to unravel soliton behavior. particularly extend into diverse domains, such as shallow water waves and optical fiber communication. The novel techniques employed in this study contribute to the stability of the exact solutions obtained, offering new perspectives beyond previous endeavors in the field. [ABSTRACT FROM AUTHOR]

This manuscript presents some new exact solutions for the dispersive Schrödinger Hirota's (SH) equation considering the effects of spatio-temporal dispersion with parabolic law nonlinearity. A wave transformation technique is implemented to transform the SH equation into a nonlinear ordinary differential equation. The solutions for the dispersive SH equation are derived using the modified extended tanh approach. These solutions exhibits various sorts of solitons, including bright, dark, periodic, and singular solitons. The findings of this research hold potential significance in the domain of fiber-optic communication, as they contribute to a deeper understanding of soliton dynamics. [ABSTRACT FROM AUTHOR]