Nonlinear Electrical Line Research Articles

Construction of Breather soliton solutions of a modeled equation in a discrete nonlinear electrical line and the survey of modulationnal Instability

The most used signals nowadays for the propagation of information in the different transmission lines are solitons because of the simple fact that they are waves of steady state that maintain their forms, their velocity and resist best on dissipative factors [–]. Contrary to the other signals, a soliton has a mathematical analytic expression obtained from nonlinear partial differential equations of integrated physical systems and permits the easy access to information relative to the type of signal, to its velocity, to its wave vector and even the characteristics of the transmission line. In this article, we are using a nonlinear line made up of a sequence of identical discrete LC electrical networks to model a discrete nonlinear differential equation which govern the dynamics of Breather solitons in the line. We then construct some solitary wave solutions of type Dark, Bright, and the combined Bright and Dark solitons of that equation by using the direct and effective mathematical method of Bogning-Djeumen Tchaho-Kofane. A numerical simulation has permitted to draw and observe the different profiles of obtained real solitons and the different profiles of their intensity. We use the analytical expressions of each of those obtained Breather solitons and the technique of perturbing steady state solution to study their modulational instability. This has permitted to obtain information on the factors that perturbate these solitons in the course of their propagation in the electrical line notably the domain of stability or the domain of instability.

Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the [formula omitted]-expansion method

This work focuses on finding soliton solutions in a nonlinear transmission line. By applying the Kirchhoff’s laws and the continuum approximation to a nonlinear electrical line, we arrive at the equation of wave propagation. Solving this equation through the Kudryashov method and the (G′/G)-expansion method provides kink, antikink and breather soliton solutions. In view of the obtained results, the Kudryashov method and the (G′/G)-expansion method are potential candidates which can be extended to other nonlinear transmission lines.

Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines

In this work, we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines. Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch. Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing. On one hand, the difference between the two lines induced the fission for only one mode of propagation. This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton, leading to a possible increasing of the bit rate. On the other hand, the dissymmetry of the two lines converts the network into a good amplifier for the ω_ mode which corresponds to the regime admitting low frequencies.

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of n-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary n-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

Modulational stability of solitary states in a lossy nonlinear electrical line

The modified Ginzburg–Landau equation that describes the pulse propagation in a lossy electrical transmission line is used to derive an eigenvalue problem that allows a detailed investigation of the modulational stability of the solitary states in the line. It is found that the growth rates of the perturbation are complex functions of the spatial variable and that, in general, the solitary states in the network can be either modulationally stable, unstable, or destabilized under a given perturbation function.

Waves Amplification in Discrete Nonlinear Electrical Lines: Direct Numerical Simulation

We study the amplification of a pulse soliton in a discrete nonlinear electrical transmission line using negative nonlinear resistances and inductances linearly varying in space. The numerical simulation is used to solve the resulting set of discrete nonlinear differential equations in each case. In both cases, the dissipative effects of the medium in which it travels are compensated on a short distance of a doped domain. During the crossing of this doped domain, the wave conserves its pulse form and recovers its amplitude when coming out.

PATTERN DYNAMICS IN A NONLINEAR ELECTRICAL LATTICE

In this paper, we present experiments using a nonlinear electrical line, modeling the FitzHugh–Nagumo equation, without recovery term. Different patterns are studied according to the parameters of this medium and initial conditions. We then propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, two kinds of binarization — one depending on an amplitude threshold, the other on an energetical threshold — and nonlinear filtering allowing noise removal can be obtained in the same medium.