Chen-Lee-Liu Research Articles

Assorted optical soliton solutions of the nonlinear fractional model in optical fibers possessing beta derivative

The nonlinear Chen-Lee-Liu (CLL) equation is an important mathematical model that is employed in the evaluation of optical fiber communication systems. It considers several factors such as noise, dispersion, and nonlinearity that might affect the signal quality and data transmission rates in optical fiber networks. The design of optical fiber systems may be optimized by using the CLL model. In this paper, we have examined adequate soliton solutions that can be applied to the optics of the CLL model with a beta derivative utilizing the auxiliary equation and advanced generalized -expansion approaches. The bell-shaped, periodic, and other soliton-like properties are displayed in the numerical simulations of the resultant solutions and the necessary forms demonstrated the structure, propagation, and impact of the fractional parameter. The findings of this study show that the applied methodologies are dependable, effective, and competent to create optical soliton solutions for additional complex wave equations in optical fiber communication.

Bright Solitons, dark solitons and periodic wave solutions of Chen–Lee–Liu model

Chen–Lee–Liu (CLL) equation has many applications in optical fibers as well as in plasma physics. It describes the propagation of optical pulse in the monomode fiber. CLL equation is a modification of the nonlinear Schrödinger equation. In this paper, the nonlinear CLL is explored using generalized projective Riccati equation method and two variable [Formula: see text]-expansion method. Consequently, many new solitary wave solutions are achieved in a unique way. These solutions include dark solitons, bright solitons and periodic wave solutions which describe the related physical phenomena. In the end, these solutions are presented in the form of 3D and 2D plots in order to elaborate the wave structure corresponding to the obtained solutions.

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.

Analyzing pulse behavior in optical fiber: Novel solitary wave solutions of the perturbed Chen–Lee–Liu equation

This study explores the novel solitary wave solutions of the perturbed Chen–Lee–Liu (CLL) equation, aiming to elucidate the physical and dynamic behaviors of pulses in optical fiber. The perturbed CLL equation is derived from the well-known Schrödinger equation and serves as an iconic model. Two analytical techniques are employed to obtain these novel solitary wave solutions. Subsequently, these solutions are subjected to objective analysis using a widely recognized semianalytical scheme to comprehend their underlying mechanisms. Multiple graphs with diverse styles are utilized to illustrate the analysis of pulse waves in optical fiber and assess the accuracy of the analysis. The scientific novelty of this research lies in providing a comprehensive explanation through a comparative analysis of our recently published results in related research papers.

Analyzing the physical behavior of optical fiber pulses using solitary wave solutions of the perturbed Chen–Lee–Liu equation

This research paper investigates the behavior of optical fiber pulses by studying the solitary wave solutions of the perturbed Chen–Lee–Liu (CLL) equation. The perturbed CLL equation is derived from the perturbed Schrödinger equation. Two analytical approaches for obtaining the innovative soliton-wave solutions are presented in this paper, and their reliability is examined by using a well-established numerical method. The accuracy of pulse wave analysis in an optical cable is demonstrated through a series of graphical representations. Our study introduces scientific novelty, as evidenced by the comparative analysis of our data with those of previous research papers. This research contributes to enhancing the understanding of the kinetics and physical behavior of pulses in optical fibers, which holds implications for the advancement of optical communication technologies.

New optical soliton solutions and dynamical wave formations for a fractionally perturbed Chen-Lee-Liu (CLL) equation with a novel local fractional (NLF) derivative

In this work, we use a novel fractional-order derivative for the fractionally perturbed Chen–Lee–Liu nonlinear equation. The new extended hyperbolic function (EHF) method is applied for obtaining new optical soliton solutions of the mentioned equation. Three-dimensional graphics and projection 3D plots are used for showing the dynamic wave formations of the soliton solutions. Then, we contrast our findings with the earlier existing results for the nonlinearly perturbed CCL. The generated solutions show that the extended hyperbolic function (EHF) method for finding soliton solutions to highly nonlinear equations is productive, suitable, and competent in optical fibers, fractional calculus, and nonlinear sciences.

Accurate computational simulations of perturbed Chen–Lee–Liu equation

This research aims to look into alternative unique solitary wave solutions to the perturbed Chen–Lee–Liu (CLL) equation to explain the kinetic and physical aspects of an optical fiber pulse. The perturbed CLL equation is one of the most well-known icon models derived from the well-known Schrödinger equation. Two different analytical methodologies are used to develop novel solitary wave solutions. These responses are then thoroughly evaluated using a well-known numerical approach to establish their underlying veracity. Various graphics are used to show the pulse wave analysis process and outcomes in an optical cable. We show how scientifically unique the study is by explaining the comparison figure that was made from our data and has been used in many recent research studies

BIFURCATION, PHASE PORTRAIT, CHAOTIC PATTERN AND TRAVELING WAVE SOLUTION OF THE FRACTIONAL PERTURBED CHEN–LEE–LIU MODEL WITH BETA TIME-SPACE DERIVATIVE IN FIBER OPTICS

In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.

Dynamics of optical pulses in birefringent fibers without four-wave mixing effect via efficient computational techniques

In this manuscript, we discuss the dynamical behavior of Chen-Lee-Liu (CLL) equation in birefringent fibers which is modeled by two-component nonlinear Schrodinger equation (NLSE) without four-wave mixing effect. In optical fibers and other wave-guide mediums this system models the propagation of soliton flow using group velocity dispersion (GVD) and self-steeping coefficients. In the realms of maritime transport, motion, and energy, the dynamics of deep-sea waves is one of oceanography’s greatest challenges. A mathematical model of the dynamics of solitary waves in the deep ocean under a two-layer stratification yields the NLSE, and resultantly, the interaction between the two can be described by a coupled NLSE. Using two recently developed integration tools, namely the generalized exponential rational function method (GERFM) and the new extended direct algebraic method (NEDAM), the various optical pulses in the forms of bright, dark, combined, and complex solitons are extracted. Moreover, the hyperbolic, exponential, and trigonometric function solutions are recovered. In addition, a comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. By choosing appropriate parameter values for numerical simulation and physical explanations, the significance of the results is demonstrated. The results of this paper can enhance the nonlinear dynamical behavior of a given system and demonstrate the suitability of the methodology employed. This research, in our opinion, will be beneficial to a wide variety of engineering model specialists.

Optical solitons via the collective variable method for the classical and perturbed Chen–Lee–Liu equations

Abstract In this article, the collective variable method to study two types of the Chen–Lee–Liu (CLL) equations, is employed. The CLL equation, which is also the second member of the derivative nonlinear Schrödinger equations, is known to have vast applications in optical fibers, in particular. More specifically, a consideration to the classical Chen–Lee–Liu (CCLL) and the perturbed Chen–Lee–Liu (PCLL) equations, is made. Certain graphical illustrations of the simulated numerical results that depict the pulse interactions in terms of the soliton parameters are provided. Also, the influential parameters in each model that characterize the evolution of pulse propagation in the media, are identified.

Investigation of optical solitons with Chen–Lee–Liu equation of monomode fibers by five free parameters

The optical solitons are extracted with Chen–Lee–Liu (CLL) equation that is considered with group velocity dispersion. The CLL equation describes the propagation of optical pulses in monomode fibers. In this article, the variety of solitons like dark, singular, dark-singular, bright-dark and periodic solutions are obtained by the mean of Fan-extended sub equation method under different constraint conditions. Moreover, for showing the physical interpretation of some recovered solutions, we also plot 3D maps by using the suitable values of involved parameters in solutions. The performance of the used method shows the adequate, validity and ability for implementation to many other nonlinear models.

Numerical investigation of the Adomian-based methods with w-shaped optical solitons of Chen-Lee-Liu equation

The present paper computationally examines the w-shaped solitary wave solutions for an important type of nonlinear Schrödinger equation that appeared in 1979 called the Chen-Lee-Liu (CLL) equation by proposing two recursive schemes. The schemes are based on the famous Adomian’s efficient decomposition technique. We successfully simulated the two proposed schemes with the aid of mathematical software and established a comparative analysis. It is noted from the present study that the improved method performs better than the classical method at different time levels. This is in fact in conformity with most of the results in the related literature. We finally present tables and a series of figures to support the presented results.

Dynamical behavior of fractional Chen-Lee-Liu equation in optical fibers with beta derivatives

This paper studies the dynamical behaviors of nonlinear wave solutions of perturbed and unperturbed fractional Chen-Lee-Liu (CLL) equation in optical fibers with a newly defined beta derivative. The coupled amplitude-phase formulation is used for the derivation of a nonlinear differential equation which contains a fifth-degree nonlinear term describing the evolution of the wave amplitude in the nonlinear system. Variety of soliton solutions are found by using the new extended direct algebraic method. Then, discussed model is converted into the planer dynamical system with the help of Galilean transformation and the bifurcation behavior is reported. All possible forms of phase portraits with respect to the parameters of the considered problem are plotted. In addition, by applying an extrinsic periodic force the effect of physical parameters is investigated. Furthermore, sensitive analysis is applied for different initial value problems to analyze the quasiperiodic and quasiperiodic-chaotic behaviors.

Numerical Consideration of Chen-Lee-Liu Equation through Modification Method for Various Types of Solitons

The purpose of the current study is to assess the effectiveness and exactness of the new Modification of the Adomian Decomposition (MAD) method in providing fast converging numerical solutions for the Chen-Lee-Liu (CLL) equation. In addition, we are able to simulate the scheme and provide a comparative analysis with the help of some exact soliton solutions in optical fibers. Finally, the MAD method uncovered that the strategy is proven to be reliable due to the elevated level of accuracy and less computational advances, as demonstrated by a series of tables and figures.

APPROXIMATE ADOMIAN SOLUTIONS TO THE BRIGHT OPTICAL SOLITARY WAVES OF THE CHEN-LEE-LIU EQUATION

The present paper examines the Chen–Lee–Liu (CLL) equation numerically. The equation is an important type of the Derivative Nonlinear Schrodinger (DNLS) equations that describe the propagation of pulse in optical fibers. The optical solitary wave solutions of the CLL equation comprises of the recently obtained bright solitons via ansatz method. However, in this paper, we employ the promising Adomian Decomposition Method (ADM) to further demonstrate its efficiency in solving different types of Schrodinger equations. The method reveals amazing approximate solutions with minimal error as shown in the respective comparison tables and various plots depicted.

Riemann–Hilbert approach andN-soliton solutions for the Chen–Lee–Liu equation

In this paper, we construct the Riemann–Hilbert problem to the Lax pair of Chen–Lee–Liu (CLL) equation. As far as we know, many researchers have studied various equations with Riemann–Hilbert method before, but no one compared the N-soliton solutions calculated by different symmetries of potential matrix. Using different symmetries of potential matrix, we get two N-soliton solution formulae of the CLL equation. The interesting thing is that we find the equivalence of these two N-soliton solutions.

Bright optical solitons of Chen-Lee-Liu equation with improved Adomian decomposition method

This research work presents some numerical the results and analyses of three types of bright soliton solutions for the Chen-Lee-Liu (CLL) equation obtained from the improved Adomian decomposition method. The error analyses of the algorithm ae also discussed.

Fission and fusion interaction phenomena of the discrete kink multi-soliton solutions for the Chen–Lee–Liu lattice equation

Chen–Lee–Liu (CLL) lattice equation is an integrable discretization of the CLL equation which can be used to model the evolution of the self-steepening optical pulses without self-phase modulation. In this paper, the discrete N-fold Darboux transformation (DT) is used to derive the discrete kink multi-soliton solutions in terms of determinant for CLL lattice equation. Soliton fission and fusion interaction structures of such solutions are shown graphically. The details of their evolution are investigated by using numerical simulations, showing that a small noise with amplitude less than or equal to 0.01 produces a strong oscillation and instability of these kink soliton solutions. The discrete generalized perturbation [Formula: see text]-fold DT is constructed to express some rational solutions in terms of the determinants of CLL lattice equation by modifying the discrete N-fold DT. Infinitely many conservation laws for CLL lattice equation are constructed based on its Lax representation. Results in this paper might be helpful for understanding the propagation of optical pulses.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation [Formula: see text]-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation [Formula: see text]-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup–Newell (KN) equation, Chen–Lee–Liu (CLL) equation and Gerjikov–Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

We consider a higher-order Chen-Lee-Liu (CLL) equation with third order dispersion and quintic nonlinearity terms. In the framework of the Riemann-Hilbert method, we obtain the compact N-soliton formula expressed by determinants. Based on the determinant solution, some properties for single soliton and asymptotic analysis of N-soliton solution are explored. The simple elastic interaction of N solitons is confirmed.