Electrical Solitons Research Articles

A complete dynamical analysis of discrete electric lattice coupled with modified Zakharov–Kuznetsov equation

The behavior of nonlinear waves within a modified Zakharov–Kuznetsov equation and their interactions with discrete electric lattice structures are examined in this study. The ϕ6−model expansion method is utilized to acquire substantial knowledge into the complex dynamics of the system under consideration, particularly with regard to the discrete electric lattice and analytical electrical solitons. By incorporating higher-order effects and improving accuracy in representing specific physical conditions, the study achieves a more realistic portrayal of nonlinear wave dynamics. The investigation also sheds light on the relationship between non-linearity, discreteness, and equation dynamics by exploring the conditions that lead to the formation of solitons and other nonlinear structures. In addition, a unique set of electrical solitons is defined to explore dynamic behaviors such as chaotic, quasi-periodic, and periodic motions under various parameterized conditions, including an external damping force. Phase plane analysis is visualized by using dynamic structure 3D and 2D phase plots, is used for bifurcation and sensitivity inspections. Finally, time series graphs are offered as mathematical depictions of solitary waves, and Lyapunov exponents with real and complex eigenvalues are used to study the stability and chaotic behaviors of the system.

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

Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation

A nonlinear electrical lattice is an effective experimental tool for dealing with nonlinear dispersive media and creating possibilities for the realistic modeling of electrical soliton. In this work, we discuss the dynamical behavior of the governing (1+1)-dimensional time–space Salerno equation, which describes the discrete electrical lattice with nonlinear dispersion. The different kinds of solutions in the form of periodic, Jacobi elliptic, and exponential functions are obtained by the two analytical approaches, namely the modified generalized exponential rational function method (MGERFM) and the extended sinh-Gordon equation expansion method (shGEEM). The MGERF approach is applied to construct exact solitary wave solutions containing trigonometry, hyperbolic and exponential functions, while the extended shGEE technique is employed to obtain periodic wave solutions containing hyperbolic and Jacobi elliptic functions via performing the symbolic computation in the software package MATHEMATICA. Moreover, by means of standard linear-stability analysis, the modulation instability (MI) and the MI gain spectrum is analytically computed for the considered equation. By selecting suitable parametric values, solution profiles are portrayed in order to make the solutions physically relevant. These results yield periodic waves, kink waves, multi-soliton, and their interactions. By comparing the obtained solutions to the previous findings, we can reveal the novelty of the solutions. In addition, all the obtained solutions were verified by substituting them back into the governing equation using the Mathematica software. The acquired results are significant for the study of wave propagation, signal transmission, and applications of super-transmission phenomena.

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.

Optical and rogue type soliton solutions of the (2+1) dimensional nonlinear Heisenberg ferromagnetic spin chains equation

In this study, the uses of unified method for finding solutions of a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the parametric requirements for the existence of a valid soliton. In order to visualize some of the discovered solutions, we plot the 2D and 3D graphics. The results of this investigation, which have been presented, might be useful in elucidating the model's physical significance. These are a highly useful tool for studying how electrical solitons, which travel as voltage waves in nonlinear dispersive media, spread out, as well as for doing various physical calculations. The study’s findings, which have been disclosed, might be useful in illuminating the models under consideration's physical significance and electrical field.

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

Nonlinear electrical lattices are powerful experimental tool for studying nonlinear dispersive media and creating opportunities for the realistic modeling of electrical solitons. In this work, we adopt the generalized auxiliary equation methods, the first integral method, and the Möbius transformation approach to extract a variety of traveling and solitary wave solutions of the nonlinear Salerno equation describing the nonlinear discrete electrical lattice with nonlinear dispersion. The kink, antikink, dark, bright, peakons, antipeakons, and periodic wave solutions are all derived. The existence criteria of solitons are described. It has been shown that for the selective values of arbitrary constants in an auxiliary equation, the generalized auxiliary equation method II is reduced to the new ‐model expansion method as well as the new extended auxiliary equation method. The impact of free parameters on the obtained solutions is investigated and graphically depicted using physical descriptions. The acquired results are important for the validity of numerical and experimental results and further understanding of the wave propagation in the nonlinear discrete electrical lattice. In addition, the stability analysis of the obtained solitary wave solutions is studied. Furthermore, using the maple software, all derived solutions were checked by re‐entering them into the considered equation.

Lie group classification of the nonlinear transmission line model and exact traveling wave solutions

A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the \(\tanh\)-method of the governing nonlinear problem.

Fractional nonlinear electrical lattice.

We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long distances, decreases as a power law. In the linear regime, we compute both the spectrum of plane waves and the mean-square displacement (MSD) of an initially localized excitation, in closed form in terms of regularized hypergeometric functions and the fractional exponent. The MSD shows ballistic behavior at long times, MSD∼t^{2} for all fractional exponents. When the fractional exponent is decreased from its standard integer value, the bandwidth decreases and the density of states shows a tendency towards degeneracy. In the limit of a vanishing exponent, the system becomes completely degenerate. For the nonlinear regime, we compute numerically the low-lying nonlinear modes, as a function of the fractional exponent. A modulational stability computation shows that, as the fractional exponent decreases, the number of electrical discrete solitons generated also decreases, eventually collapsing into a single soliton.

Analytical modeling of electrical solitons in a nonlinear transmission line using Schamel–Korteweg deVries equation

Abstract Nonlinear transmission lines (NLTLs) provide an effective means of experimental investigation of nonlinear dispersive media paving the way for accurate modeling of electrical solitons. In this work, an appropriate analytical model is proposed to analyze and predict electrical solitons in an NLTL. The model is based on a new form of nonlinearity which utilizes fractional powers to render an accurate representation of the Capacitance-Voltage (C-V) curve, even for relatively higher voltages. A complete analytical procedure is adopted to obtain the soliton solution in an NLTL. Nonlinear analysis results in a Schamel type Korteweg deVries (S-KdV) equation, instead of a conventional KdV equation. An extended version of the Tanh method is employed to find the solution of S-KdV which yields narrower solitons of Sech4 shape. The proposed model is validated experimentally by using a specially designed NLTL (100 sections) comprising of linear inductors and nonlinear capacitances. Square pulses with a repetition rate of 100 kHz are used to generate the solitons. The comparative analysis shows excellent profile matching between theoretically predicted and experimentally obtained solitons. Furthermore, in consistence with the prediction of the proposed model, the product of the Amplitude and fourth power of the Width (A × W4) is found to be constant in experimental results. This model proposed in the present work can be of help in understanding and predicting the behavior of electrical solitons in NLTLs.

Leapfrogging of electrical solitons in coupled nonlinear transmission lines: effect of an imperfect varactor

The leapfrogging dynamics of a pair of electrical solitons is investigated, by considering two capacitively coupled nonlinear transmission lines with and without intraline resistances. We discuss two distinct transmission line set-ups: in the first, we assume two RLC ladder lines with intraline varactors and a coupling linear capacitor, and in the second, we consider two capacitively coupled lossless lines with a varactor carrying impurity (imperfect diode) in one of the two interacting transmission lines. In the first context, we find that the soliton-pair leapfrogging mimics the motion of a damped harmonic oscillator, the frequency and damping coefficient of which are obtained analytically. Numerical simulations predict leapfrogging of the soliton pair when the differences in the initial values of the amplitude and phase are reasonably small, and the resistance is not too large. In the second context, leapfrogging occurs when the impurity rate is small enough and the differences in the initial values of the amplitude as well as phase are also small. As the impurity rate increases, the soliton signal in the imperfect line gets accelerated upon approaching the defective diode, causing only this specific soliton signal to move faster than its counterpart, leading to the suppression of leapfrogging.

Electrical Solitons for Microwave Systems: Harmonizing Nonlinearity and Dispersion with Nonlinear Transmission Line

Nonlinearity and dispersion are often nuisances that microwave engineers seek to curb. However, there is a system that can harmonize these two effects to produce useful-and fascinating-dynamics with unique microwave engineering opportunities: the nonlinear transmission line (NLTL) [1]-[11]. The NLTL is a ladder network of lumped inductors and varactors [Figure 1(a)] that can be alternatively built by periodically loading a smooth transmission line with lumped varactors [Figure 1(b)].

Exact solitary wavelike solutions in a nonlinear microtubule RLC transmission line.

Analytically, we study the dynamics of ionic waves in a microtubule modeled by a nonlinear resistor, inductor, and capacitor (RLC) transmission line. We show through the application of a reductive perturbation technique that the network can be reduced in the continuum limit to the dissipative nonlinear Schrödinger equation. The processes of the modulational instability are studied and, motivated with a solitary wave type of solution to the nonlinear Schrödinger (NLS) equation, we use the direct method and the Weierstrass's elliptic function method to present classes of solitary wavelike solutions to the dissipative NLS equation of the network. The results suggest that microtubules are the biological structures where short-duration nonlinear waves called electrical envelope solitons can be created and propagated. This work presents a good analytical approach of investigating the propagation of solitary waves through a microtubule modeled by a nonlinear RLC transmission line.

Dynamics of modulated waves in a nonlinear microtubule RLC transmission line

We study the dynamics of modulated ionic waves in a microtubule modeled by a nonlinear RLC transmission line (Tuszynski et al., 2004; Sataric et al., 2009). We show through the application of a reductive perturbation technique that the network can be reduced in the continuum limit to the dissipative nonlinear Schrödinger equation. The processes of the modulational instability and the effects of the dissipative elements of the network on wave propagation are investigated. We perform numerical simulations which confirm analytical predictions and give rise to localized modulated wave formation. The results suggest that microtubules can be biological structures where short-duration nonlinear waves called electrical envelope solitons can be created and propagated.

Perspective: Strong microwave photon-magnon coupling in multiresonant dielectric antennas

Achieving quantum-level control over electromagnetic waves, magnetisation dynamics, vibrations, and heat is invaluable for many practical applications and possible by exploiting the strong radiation-matter coupling. Most of the modern strong microwave photon-magnon coupling developments rely on the integration of metal-based microwave resonators with a magnetic material. However, it has recently been realised that all-dielectric resonators made of or containing magneto-insulating materials can operate as a standalone strongly coupled system characterised by low dissipation losses and strong local microwave field enhancement. Here, after a brief overview of recent developments in the field, I discuss examples of such dielectric resonant systems and demonstrate their ability to operate as multiresonant antennas for light, microwaves, magnons, sound, vibrations, and heat. This multiphysics behavior opens up novel opportunities for the realisation of multiresonant coupling such as, for example, photon-magnon-phonon coupling. I also propose several novel systems in which strong photon-magnon coupling in dielectric antennas and similar structures is expected to extend the capability of existing devices or may provide an entirely new functionality. Examples of such systems include novel magnetofluidic devices, high-power microwave power generators, and hybrid devices exploiting the unique properties of electrical solitons.

Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals.

A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge ‘soakage’ is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge ‘soakage’) have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell’s equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.

Soliton solutions and conservation laws for lossy nonlinear transmission line equation

In this article, the Lie symmetry and Ricatti-Bernoulli (RB) sub-ODE method are applied to obtain soliton solutions for nonlinear transmission line equation (NLTLs). The NLTLs is defined to be a structure whereby a short-duration pulses known as electrical solitons can be invented and disseminated. We compute conservation laws (Cls) via a non-linear self-adjointness approach. A suitable substitution for NLTLs is found and the obtained substitution makes the NLTLs equation a non-linearly self-adjoint. We establish Cls for NLTLs equation by the new Cls theorem presented by Ibragimov. We obtain trigonometric, algebraic and soliton solutions. The obtained solutions can be useful for describing the concentrations of transmission lines problems, for NLTLs. The parameters of the transmission line play a significant role in managing the original form of the soliton.

Exact and soliton solutions to nonlinear transmission line model

A nonlinear transmission line (NLTL) is comprised of a transmission line periodically loaded with varactors, where the capacitance nonlinearity arises from the variable depletion layer width, which depends both on the DC and AC voltages of the propagating wave. An equivalent circuit model of NLTL is discussed analytically, in this article, and different type of solutions are celebrated. The improved extended tanh-function method has been applied successfully to extract the solutions. The obtained solutions are solitary wave solutions, singular periodic solutions, singular soliton solutions, Jacobi elliptic doubly periodic type solutions and Weierstrass elliptic doubly periodic type solutions. It is a very convenient tool to study the propagation of electrical solitons which propagate in the form of voltage waves in nonlinear dispersive media.

High-dimensional chaos from self-sustained collisions of solitons

We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.

Study of electrical soliton as transmission pulse for UWB communication

This paper introduced soliton phenomena in nonlinear transmission line,analyzed the principle of electrical soliton and electrical soliton oscillator,and also gave a simulation experiment under the restrictions of bandwidth and emission power permitted by Federal Communications Commission(FCC).The simulation results show that the electrical soliton signal can be used as transmission pulse for UWB.

High-Power Pulsed RF Extraction From Nonlinear Lumped Element Transmission Lines

Electrical soliton bursts are generated on a range of simulated and experimental nonlinear lumped element transmission lines (NLETLs). The design parameters necessary to achieve high frequency waveforms with peak voltage amplification are investigated, and the control over output frequency is demonstrated. An explanation of the fundamental problem of extracting extended bursts of solitons to linear load resistances is offered, along with the results from successful novel NLETL-based soliton burst generators tested at low voltages.