Pulse Propagation In Optical Fibers 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.

Exploring the impact of multiplicative white noise on novel soliton solutions with the perturbed Triki–Biswas equation

This study examines the effects of multiplicative white noise on soliton perturbations governed by the Triki–Biswas equation for the first time. Triki–Biswas equation advances research on ultrashort pulse propagation in optical fibers. It modifies the nonlinear Schrödinger equation to describe the behavior of femtosecond pulses more accurately in optical media, becoming a critical tool in the field. The paper employs two innovative methods, the enhanced direct algebraic method and the new projective Riccati equations method to uncover a broad range of soliton solutions, including bright, dark, and singular solitons. The solutions are expressed in terms of Jacobi elliptic functions and exhibit a transition to soliton-type solutions as the elliptic modulus approaches unity. This investigation is the first of its kind to explore the effects of multiplicative white noise within this context, providing new perspectives and methodologies for future research in the field. The study sheds light on previously unexplored aspects of multiplicative white noise and contributes significantly to the body of knowledge in soliton theory and its application to optical fiber technology.

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.

A Kundu-nonlinear Schrödinger equation: Rogue waves, breathers, and mixed interaction solutions.

A Kundu-nonlinear Schrödinger equation that can be utilized to simulate the pulse propagation in optical fibers is researched in this paper. First, the Lax integrability of the above equation is proved and its modulational instability (i.e., the main mechanism for producing the rogue wave solutions and the breather solutions) is calculated. Subsequently, using the generalized perturbation (n,N-n)-fold Darboux transformation, the rogue waves, breathers, and mixed interaction solutions are acquired, as well as the impact of various parameters on the solutions is examined. In particular, when we assume that the coefficient of the equation is θ=mx+dt, some new wave structures are found based on parameter variations, such as the rotational separation of first-order rogue waves, scale-like structures generated by second-order breathers, etc., which offer novel ideas for producing different signals via optical fibers. Ultimately, the classification numbers of mixed solutions of rogue waves and breathers are provided, which can better observe how the two types of the local waves are combined, in accordance with the distributions of the increasing numbers of algebraic equations.

Explicit optical solitons of a perturbed Biswas–Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

This paper deals with a new variant of the Biswas–Milovic equation, referred to as the perturbed Biswas–Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Utilizing a wave transformation technique on the considered Biswas–Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas–Milovic equation, are derived by resolving this system. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.

Bright soliton of Stochastic perturbed Biswas-Milovic equation with cubic-quintic-septic law having multiplicative white noise

For the first time, the adopted stochastic form of the perturbed Biswas-Milovic equation with cubic-quintic-septic law having spatio-temporal and chromatic dispersion in the presence of multiplicative white noise in Ito sense was presented and examined. The Biswas-Milovic equation ˆ models numerous physical phenomena occurring in optical fiber. We analyzed the optical soliton solutions of the stochastic model with the aid of a subversion of the new extended auxiliary equation method. Furthermore, we investigated the evaluation of the noise impacts and the effects of some model parameters on the dynamics of the generated soliton. Finally, graphical depictions of the derived soliton types were represented for some solution functions. The stochastic model and the derived results will contribute to the comprehension of the nonlinear dynamics of pulse propagation in optical fibers which has great importance for the advancement of optical communication engineering.

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

A comprehensive analysis of Fokas–Lenells equation using Lie symmetry method

This article extracts analytical solutions of the Fokas–Lenells equation describing pulse propagation in optical fibers and presents a comprehensive analysis of the analytical solutions. This paper focuses on deriving analytical, non‐perturbative solutions for the Fokas–Lenells equation by reducing it to a system of ordinary differential equations using the Lie symmetry method. Three generators for the Lie algebra are obtained, and three reductions are explored by combining vector generators. These algebraic structures provide a powerful framework for simplifying complex mathematical and physical problems by revealing underlying symmetries and patterns. The graphical representations of obtained solutions are rendered. Besides, the influence of parameters within the equation on the behavior of the solutions has been demonstrated in the figures. These results contribute to a deeper understanding of the Fokas–Lenells equation and have implications in various fields of physics and engineering.

Analytical soliton solutions for cubic-quartic perturbations of the Lakshmanan-Porsezian-Daniel equation using the modified extended tanh function method

In this paper, the improved modified extended Tanh function technique is used to find analytical solutions to the cubic-quartic Lakshmanan-Porsezian-Daniel model which describes the pulse propagation in optical fiber. Using the traveling wave theory, the nonlinear partial differential form of the cubic-quartic Lakshmanan-Porsezian-Daniel equation is transformed into an ordinary differential equation. Then applying the proposed methods bright, dark, bright-dark, periodic, singular, and Jacobian elliptic solutions were derived as analytical solutions. Besides, hyperbolic, rational, trigonometric, and exponential functions were also obtained. In order to understand the obtained solutions, graphical simulations were depicted by 3D surfaces and 2D graphs.

Exact chirped solutions of perturbed Chen-Lee-Liu equation with refractive index

We study the exact chirped solutions of the perturbed Chen-Lee-Liu equation with a refractive index. Exact chirped solutions and their corresponding chirps are obtained using trial equation method and complete discrimination system for polynomial. Illustrations are presented under certain parameter conditions. Chen-Lee-Liu model describes pulse propagation in optical fibers. Studying chirped solutions to the perturbed Chen-Lee-Liu equation with a refractive index could improve the understanding of physical phenomena and may have applications in the design of optical fibers.

Optical fiber application of the Improved Generalized Riccati Equation Mapping method to the perturbed nonlinear Chen-Lee-Liu dynamical equation

This work considers the improved generalized Riccati equation mapping (IGREM) technique with its Bäcklund transformation to obtain the wave solutions of the perturbed Chen-Lee-Liu (CLL) equation. The CLL equation actually depicts pulse propagation in optical fibers and plasma. We utilize proposed technique to obtain hyperbolic, periodic trigonometric, rational and exponential function solutions. To make this work worthy and for efficient illustration of this methodology, 3D, contours and 2D plots of some selected solutions are constructed by selecting the values of involved parameters. The results of this paper prove that the used method is effective to improve the nonlinear dynamical behavior of a system.

Wide-spectrum optical soliton solutions to the time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law

The time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law and its soliton solutions have significant implications to examine the dynamics of optical solitons, self-phase modulation, optical beam propagation in nonlinear media, pulse propagation in optical fibers, nonlinear waveguides, and signal transmission systems. This study focuses on the investigation of different soliton solutions related to various aspects of optical solitons, including their formation, propagation traits, and stability analysis of the mentioned equation. Soliton solutions are able to carry out long-distance transmission without frequent amplification and regeneration. We exploit an advanced mathematical technique, the (G′/G,1/G)-expansion method to descend and analyze the soliton solutions. As a result, a significant number of definitive and efficient solitons, such as compacton, bell-shaped, anti-peakon, breather, periodic, and singular solitons have resulted. The uniqueness of the obtained solutions is established by comparing them with previous results. Also, we discuss in detail the implications of fractional derivative and the application of the obtained solutions to optical fiber communication and other relevant fields. The findings of the present study provide valuable insights into the fundamental nature of optical solitons. These insights will contribute to the design and optimization of future optical networks, enabling the development of faster, more reliable, and higher-capacity communication systems.

Traveling Wave Optical Solutions for the Generalized Fractional Kundu–Mukherjee–Naskar (gFKMN) Model

The work considers traveling wave optical solutions for the nonlinear generalized fractional KMN equation. This equation is considered for describing pulse propagation in optical fibers and communication systems using two quite similar approaches, based on the expansion of these solutions in the exponential or polynomial forms. Both approaches belong to the direct solving class of methods for PDEs and suppose the use of an auxiliary equation. The solutions acquired in this paper are obtained from first- and second-order differential equations that act as auxiliary equations. In addition, we generated 3D, contour, and 2D plots to illustrate the characteristics of the obtained soliton solutions. To create these plots, we carefully selected appropriate values for the relevant parameters.

On the dynamics of a dual space–time fractional nonlinear Schrödinger model in optical fibers

The nonlinear Schrödinger equation (NLSE) is a significant nonlinear complex model known as the most important struture to represent light pulse propagation in optical fibers, which plays a key role in demonstrating the proliferation specifically short pulse in optical fibers and have large appliances in telecommunication system and ultra fast signal routing in nonlinear optics. In this study, we look into explicit solutions of a coupled fractional NLSE for a dual space–time, which reflect numerous explicit travelling wave solutions, as well as their physical interpretation. We use the fractional complex transform to obtain multiple exact answers using the unified technique and the extended simple equation method. These exact answers include trigonometric function solutions as well as dark, bright, singular, periodic, and optical soliton solutions. For a set of appropriate parameters, Mathematica is used to represent the dynamics of various wave structures as 3D, 2D, and contour visualizations. These findings show that the proposed methodologies are simple, prolific, and capable of studying the nature of numerous physical models of complex phenomena in modern science.

Dynamical behaviors of solitons for NLSE with Kudryashov’s sextic power-law of nonlinear refractive index using improved modified extended tanh-function method

The higher order nonlinear Schrödinger equation (NLSE) describes ultrashort pulse propagation in optical fibres. In this paper, we discuss analytically the non-linear schrödinger equation with higher order dispersion terms up to sixth order and sextic power law of nonlinearity with the help of the improved modified extended tanh-function scheme. New families of solutions, such as dark solitons, singular solitons, rational solutions, periodic solutions and exponential type solutions, have been extracted. Extracted solutions will be useful in the development of the communication systems. Furthermore, some solutions are graphically depicted to demonstrate their physical nature by using distinct values of the parameters.

Solitons collision and multi-peak solutions for a new $$(3+1)$$-dimensional NLSE describing pulse propagation in optical fibers

Solitons collision and multi-peak solutions for a new $$(3+1)$$-dimensional NLSE describing pulse propagation in optical fibers

Novel soliton wave solutions of a special model of the nonlinear Schrödinger equations with mixed derivatives

In this study, the influence of the integrability requirement on nonlinear Schrödinger equations with mixed derivatives is examined. The Rangwala–Rao (RR) equation is named after A. Rangwala, who in 1990 was the first to quantify these effects in their entirety. The aim of our research is identifying how to generate individual waves and how they interact with one another. This is to get a better understanding of the dispersion effect and the progressive variation of the electric field envelope during pulse propagation in optical fibers. The direct algebraic method (DAM), the extended direct algebraic approach (exDAA), and the extended Riccati expansion technique (exREM) are used to develop unique solitary wave solutions for the model under consideration. These numerically calculated solutions illustrate the dynamic behavior of an optical pulse traveling through a cable. Comparing our results to those of other researchers demonstrates the originality of our work.

Construction of Novel Bright-Dark Solitons and Breather Waves of Unstable Nonlinear Schrödinger Equations with Applications

The unstable nonlinear Schrödinger equations (UNLSEs) are universal equations of the class of nonlinear integrable systems, which reveal the temporal changing of disruption in slightly stable and unstable media. In current paper, an improved auxiliary equation technique is proposed to obtain the wave results of UNLSE and modified UNLSE. Numerous varieties of results are generated in the mode of some special Jacobi elliptic functions and trigonometric and hyperbolic functions, many of which are distinctive and have significant applications such as pulse propagation in optical fibers. The exact soliton solutions also give information on the soliton interaction in unstable media. Furthermore, with the assistance of the suitable parameter values, various kinds of structures such as bright-dark, multi-wave structures, breather and kink-type solitons, and several periodic solitary waves are depicted that aid in the understanding of the physical interpretation of unstable nonlinear models. The various constructed solutions demonstrate the effectiveness of the suggested approach, which proves that the current technique may be applied to other nonlinear physical problems encountered in mathematical physics.

Computational Traveling Wave Solutions of the Nonlinear Rangwala–Rao Model Arising in Electric Field

The direct influence of the integrability requirement on mixed derivative nonlinear Schrödinger equations is investigated in this paper. A. Rangwala mathematically formalized these effects in 1990 and dubbed this form the Rangwala–Rao (RR) equation. Our research focuses on innovative soliton wave solutions and their interactions in order to provide a clear picture of the slowly evolving envelope of the electric field and pulse propagation in optical fibers in terms of the dispersion effect. For creating unique solitary wave solutions to the investigated model, three contemporary computational strategies (extended direct (ExD) method, improved F–expansion (ImFE) method, and modified Kudryashov (MKud) method) are employed. These solutions are numerically computed to demonstrate the dynamical behavior of optical fiber pulse propagation. The originality of the paper’s findings is proved by comparing our results to previously published results.

Optical soliton solutions of (1 + 1)- and (2 + 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies.