Nonlinear Electrical Transmission Line Research Articles

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

This paper introduces novel traveling wave solutions for the (1+1)-dimensional nonlinear telegraph equation (NLTE) and the (2+1)-dimensional nonlinear electrical transmission line equation (NETLE). These equations are pivotal in the transmission and propagation of electrical signals, with applications in telegraph lines, digital image processing, telecommunications, and network engineering. We applied the improved tanh technique combined with the Riccati equation to derive new solutions, showcasing various solitary wave patterns through 3D surface and 2D contour plots. These results provide more comprehensive solutions than previous studies and offer practical applications in communication systems utilizing solitons for data transmission. The proposed method demonstrates an efficient calculation process, aiding researchers in analyzing nonlinear partial differential equations in applied mathematics, physics, and engineering

Solitary waves of M-fractional low-pass nonlinear electrical transmission line model arising in network system

In this study, we analyze the solitary wave behavior of a truncated M-fractional low-pass nonlinear electrical transmission line (NLETLs) model. NLETL models are relevant to computer network systems, particularly for high-speed data transmissions. They influence the behavior of signals traveling through network cables. To investigate the dynamics of solitary waves in the model, we applied the modified Sardar sub-equation and extended the sinh-Gordon equation expansion methods. We illustrated the 2D, 3D, and contour shapes of selected solutions for appropriate values of the NLETLs dynamics using Mathematica-14. Kink, anti-kink, bright-dark bell, dark bell, M-shaped periodic soliton, and logarithmic wave solutions were obtained. The results indicate that the proposed techniques may provide valuable, powerful, and efficient insights into the dynamics of nonlinear evolution models. The role of the fractional order derivative in making optical solutions is investigated in detail, which opens up opportunities for the creation of more complex models that can more accurately simulate optical phenomena in the real world.

New interactions between various soliton solutions, including bell, kink, and multiple soliton profiles, for the (2+1)-dimensional nonlinear electrical transmission line equation

New interactions between various soliton solutions, including bell, kink, and multiple soliton profiles, for the (2+1)-dimensional nonlinear electrical transmission line equation

Exploring dynamic behaviors of diverse electrical soliton pulses in lossy nonlinear electrical transmission lines: Insights from analytical method and linear stability analysis technique

Exploring dynamic behaviors of diverse electrical soliton pulses in lossy nonlinear electrical transmission lines: Insights from analytical method and linear stability analysis technique

Dynamical analysis of optical soliton structures for wave propagation in nonlinear low-pass electrical transmission lines under effective approach

Dynamical analysis of optical soliton structures for wave propagation in nonlinear low-pass electrical transmission lines under effective approach

Dynamic analysis of the effects of dissipative elements and modulational instability in a multicoupled nonlinear electrical transmission line with the propagation of new rogue waveforms

In this study, we consider a nonlinear multicoupled discrete electrical transmission line consisting of several modified Noguchi lines and analyze the dynamics of the effects of dissipative elements on modulated waves. This analysis shows that the dispersion element (C S ) and solution parameter (γ) strongly contribute to the increase in voltage amplitudes and to the modulation of these new rogue waveforms, unlike the dissipative element (G). Using a semi-discrete approximation, we demonstrate that the dynamics of modulated waves in such a dissipative electrical system can be governed by a system of nonlinear Schrödinger equations, the Manakov system, and system parameters. The phenomenon of modulational instability in this dissipative electrical system is studied, and areas of instability are shown. We found that the dissipative element of this system increased and decreased the areas of instability. Under the condition of this Manakov system, we determine the approximate modulated wave solutions that are then used for the dynamic analysis of the effects of dissipative elements when transmitting these new rogue waveforms through this dissipative electrical system. The effects of the parameters of this nonlinear dissipative electrical system, such as dispersive, dissipative, and solution parameters, in the dominant direction of propagation of these new rogue wave signals are presented. Based on these results, we observe that the effects of dissipative elements do exist in this nonlinear dissipative electrical system and that these dissipative elements would also impact the areas of modulational instability, which could gradually disappear in this electrical system.

Multiple optical soliton solutions for wave propagation in nonlinear low-pass electrical transmission lines under analytical approach

Multiple optical soliton solutions for wave propagation in nonlinear low-pass electrical transmission lines under analytical approach

Exploring dynamic behaviors of soliton-like pulses in the lossy electrical transmission line model with fractional derivatives: A comparative study

This study aims to explore the intricate behavior of soliton-like pulses within a nonlinear and lossy electrical transmission line. The transmission line is described by a mathematical model called the “beta derivative”, which is specifically designed to characterize the propagation of electrical solitons in media with both nonlinearity and dispersion properties. To achieve this goal, the (G′/G2)-expansion method is applied to a periodically loaded nonlinear beta derivative lossy transmission line with symmetric voltage-dependent capacitances. Soliton-like pulses, including periodic singular, dark, bright, and singular waves, are obtained using the (G′/G2)-expansion method based on the voltage equation. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying relevant equations are provided to understand the underlying mechanisms of the soliton family. In terms of fractionality, the profiles of dark or bright waveforms maintain their complete forms, but their smoothness increases as the fractional parameters increase. On the other hand, periodic wave solutions exhibit an increase in periodicity. By adjusting the parameters of the model, the characteristics of the waves can be modified to generate desired wave profiles. Additionally, the study involves a comprehensive comparison among solutions derived from models incorporating the beta, conformable, and M−truncated derivatives. It examines how the amplitude of the solitons is influenced by the fractional parameter, utilizing graphs to visualize this impact by assigning specific fractional parameter values. These pulse-like solitons offer promising potential for integration within telecommunication systems, where they can function as information carriers, facilitating heightened data bit rates. By leveraging the findings of this study, advancements in telecommunication technology can be pursued, leading to enhanced efficiency and improved performance.

Further physical research about soliton structures and phase portraits in nonlinear fractional electrical transmission line model

This paper presents several novel contributions in the field of nonlinear fractional low-pass electrical transmission line model (NFLETLM). Firstly, using the modified (G′G2)-expansion method and the extended modified Jacobi elliptic expansion method, we discovered new and accurate solutions for NFLETLM, which have not been reported in the existing literature (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). These solutions, denoted as U3,U4,U7,U8,U9,U10,U13,U14 and UJ1,UJ2,UJ3,UJ4 represent novel contributions to the fields. Secondly, by utilizing computer simulations, we observed various intriguing phenomena in the wave solution graphs, such as anti-kink waves, periodic waves, intense singular periodic waves, bright singular wave solutions, multi-periodic waves, intense double periodic waves, and alternating patterns of light and shade waves. These findings shed light on previously unexplored aspects of the problem. Thirdly, through an extensive study on the newly discovered solutions, we provided a comprehensive understanding of the solitons inherent in the NFLETLM, including comparison with other derivative solutions. Our conformable fractional derivative solutions showed similarities to beta derivative solutions, distinguishing them from Riemann–Liouville derivative solutions. Lastly, we explored the phase portrait, bifurcation analysis, sensitivity, and potential chaotic behaviors of the NFLETLM, which have not been addressed in previous works (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). This innovative contribution expands our understanding of the NFLETLM model and uncovers new dynamics and phenomena.

Mathematical modeling of chirped modulated waves along a multi-coupled nonlinear electrical transmission line with dispersive elements

This work presents a mathematical modeling of chirped modulated waves propagating along a two-dimensional nonlinear electrical transmission line consisting of nonlinear dispersive and purely nonlinear capacitive elements. Combining the rotating-wave approximation technique with the perturbation method, we derive a two-dimensional extended nonlinear Schrödinger equation with self-steepening and self-frequency shift, that predicts the formation and propagation of a very rich variety of soliton-like waves including bright, dark, kink, and double-kink soliton-like waves with nonlinear chirp in a multi-coupled nonlinear electrical transmission network with dispersive elements. Using this model equation, parameter domains are delineated in which these modulated waves exist. The parameter domains are found to be strongly dependent on the dispersive elements of the network system. Through exact solutions of the amplitude equation, we investigate the dynamics of chirped modulated waves along the network system under consideration. Our results show that the nonlinear chirp associated with each of the found soliton-like pulses is directly proportional to the wave intensity and is saturated at some finite value as the propagation coordinate approaches its asymptotic value. Also, we show that increasing the number of the network lines decreases the propagating speed of the soliton-like pulses. Most importantly, theoretical analysis show that chirping of found network pulses can be controlled by varying the self-steepening term and self-frequency shift. The validity of analytical results and the robustness of these chirped soliton-like voltage signals which may have important applications in signal processing systems are confirmed by numerical simulations. The results of our study may be launched in long distance telecommunication lines involving higher-order nonlinearities of the fiber.

Modulation instability and modulated wave patterns in a nonlinear electrical transmission line with the next-nearest-neighbor coupling

In this paper, we investigate modulation instability and solitary waves in a one-dimensional nonlinear electrical transmission line with second-neighbor interactions. Through the quasi-discrete multiple scale method, we derive coupled nonlinear Schrödinger equations. To investigate the modulation instability in the structure, we use the linear stability analysis, and an expression for the modulation instability spectrum is derived. From the analytical investigation, we show that the second neighbor coupling affects both the modulation instability growth rate and modulation instability bands. Furthermore, we show via single and coupled mode excitation that bright and dark solitary waves can propagate at the lower and upper cutoff frequencies. To evaluate the robustness of the analytical investigation, we use a direct numerical simulation of the continuous wave. We conclude that the second-neighbor couplings generate rogue waves in the structure during the long-time evolution of the plane wave. We also demonstrate that with a variation of the excitation wave number, the nonlinear electrical transmission line can support new objects as wave molecules for high values of the wave number. This feature is not yet observed in nonlinear electrical transmission lines and will be useful in many fields of physics.

Solution Structures of an Electrical Transmission Line Model with Bifurcation and Chaos in Hamiltonian Dynamics

Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed [Formula: see text]-dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles [Formula: see text], [Formula: see text]. The most important thing is that there are iterative ideas in finding the solution process, which have not been seen before from relevant articles such as [Tala-Tebue et al., 2014; Fendzi-Donfack et al., 2018; Ashraf et al., 2022; Ndzana et al., 2022; Halidou et al., 2022] in seeking for exact solutions about NFETLE.

W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using the Jacobi elliptic function and the auxiliary equation methods. We obtain Jacobi elliptic function solutions as well as kink, bright, dark, and W-shaped solitons as a result. For specific values of the Jacobi elliptic modulus, we depict bright, dark, and W-shaped soliton solutions as suitable parameters of the structure. Using the auxiliary equation method gives the combined bright–bright and dark–dark optical solitons in optical fibers. One result emerges from this analysis: the potential parameters and free parameters of the method can be employed to degenerate W-shaped bright and dark solitons. The acquired results are general and can be used for many applications in nonlinear dynamic systems.

Diverse Soliton Structures of the ( 2 + 1 )-Dimensional Nonlinear Electrical Transmission Line Equation

In this work, the ( 2 + 1 )-dimensional nonlinear electrical transmission line equation (NETLE) is investigated by applying three recent technologies, namely, the variational approach, Hamiltonian approach, and energy balance approach. Diverse exact soliton solutions such as the bright, bright-like, kinky bright, bright-dark soliton, and periodic soliton solutions are successfully constructed. The outlines of the different solutions are shown in the form of the 3-D plot with the help of the Wolfram Mathematica. It reveals that the used methods are concise and effective and are expected to provide some inspiration for the study of travelling wave solutions of the PDEs in physics.

Soliton-mediated ionic pulses and coupled ionic excitations in a dissipative electrical network model of microtubules

Many cellular activities are mediated by microtubules (MTs), with most electrophysiological processes depending on ionic flow through MT cylinders. This paper addresses such conductive features by representing the MT as a nonlinear electrical transmission line composed of capacitive and dissipative properties. Thanks to the semi-discrete approximation near the continuum limit, coupled ionic pulses flowing along cellular microtubules are described by a set of coupled cubic complex Ginzburg-Landau (CGL) equations whose one of the solutions is a plane wave. The stability of the latter is checked, under weak modulation, using an explicit analytical expression for the modulational instability (MI) growth rate. The parametric analysis of the instability growth rate allows detecting parameter regions where ionic conductivity, through modulated waves, in the MT network is likely to occur. Dissipative bright-bright pulse soliton solutions for the nonlinearly coupled cubic CGL equations are constructed using a modified Hirota's bilinear method. A generalized coupled mode for the discrete ionic signal is proposed and used as the initial condition to be propagated in the nonlinear electrical transmission lattice of MT under direct numerical simulations. The ionic pulse transfer, mediated by the nonlinear interaction between oscillatory modes, is manifested by the formation of trains of modulated waves whose behaviors depend on the right choice of system parameters. Those results theoretically suggest that coupled ionic signals may facilitate information processing involving MTs.

A Study of the Soliton Solutions with an Intrinsic Fractional Discrete Nonlinear Electrical Transmission Line

This study aims to identify soliton structures as an inherent fractional discrete nonlinear electrical transmission lattice. Here, the analysis is founded on the idea that the electrical properties of a capacitor typically contain a non-integer-order time derivative in a realistic system. We construct a non-integer order nonlinear partial differential equation of such voltage dynamics using Kirchhoff’s principles for the model under study. It was discovered that the behavior for newly generated soliton solutions is impacted by both the non-integer-order time derivative and connected parameters. Regardless of structure, the fractional-order alters the propagation velocity of such a voltage wave, thus bringing up a localized framework under low coupling coefficient values. The generalized auxiliary equation method drove us to these solitary structures while employing the modified Riemann–Liouville derivatives and the non-integer order complex transform. As well as addressing sensitivity testing, we also investigate how our model’s altered dynamical framework shows quasi-periodic properties. Some randomly selected solutions are shown graphically for physical interpretation, and conclusions are held at the end.

Multi-wave, M-shaped rational and interaction solutions for fractional nonlinear electrical transmission line equation

In this paper, (2+1)− dimensional nonlinear fractional electrical transmission line equation (NLFETLE), which explains the wave variation in nonlinear systems, will be investigated. To convert our model into an ordinary differential equation (ODE) we adopt a conformable fractional (CF) operator. By combining exponential, polynomial, trigonometric, and hyperbolic functions, we will analyze multi-waves, periodic cross-kink, M-shaped rational and interaction solutions. We will also analyze degeneracies of hybrid waves through some graphical shapes.

On some new analytical solutions to the (2+1)-dimensional nonlinear electrical transmission line model

In the present paper, from the field of communications in physics and engineering, we select the (2+1)-dimensional nonlinear electrical transmission line equation to be studied. The model under study is one of the models that has important applications in the field of physics and telecommunications engineering. We acquire the soliton solutions by using two simple methods. We present some figures in two and three dimensions to show that these solutions actually have the properties of soliton waves.

Rational W-shape solitons on a nonlinear electrical transmission line with Josephson junction

This paper examines envelope solitons, rational W-shape solitons to a Nonlinear Electrical Transmission Line (NETL) with Josephson junction (JJ) that consist of the Nth cells of circuits. By employing the reductive perturbation approach in the semi-discrete approximation, we obtain the nonlinear Schrödinger equation (NLSE). From this equation, the frequency ranges of propagation of bright and dark solitons were obtained. As in most of the works, the NLSE obtained is well known as the seat of rogue waves and Peregrine solitons. The nonlinearity provided by the JJ, combined with the dispersion, made it possible to study the Modulation Instability (MI) gain spectrum. The 3D and 2D graphical representations illustrated the instability zones and the W-rational solutions have followed by using numerical simulation. The results obtained in this paper are of a very capital contribution for the study of rogue waves in nonlinear transmission lines or other physical problems.

Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line