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

Abstract

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.

Nonlinear localized modes in two-dimensional electrical lattices

“…Also, a phenomenological dissipation resistor, R l , was included in the model to better approximate the experimental dynamics, and its value has been determined by matching the numerical and experimental nonlinear resonance curves corresponding to a single element [24]. A simplified set of equations corresponding to the nonblock capacitor case can be obtained by considering the limit C f → ∞.…”

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

“…Modulational instability (MI) induced by the interplay between nonlinearity and dispersion (in the temporal domain) or diffraction (in the spatial domain) is a generic phenomenon in nonlinear physics [1][2][3][4][5][6][7][8][9][10]. The slow modulation of a monochromatic plane wave in the system leads to exponential growth of the unstable modes and eventually may result in the formation of envelope soliton train.…”

Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities

“…[14]). Up to now much effort has gone into their stabilization [10][11][12]15], and it's well clear that stable multibreathers can be found. Could we obtain stable multibreathers in the exciton dynamics modeled by DNLS equation with competitive nonlinearities?…”

“…[7], and since this work a great deal of effort has been invested to show their existence in Salerno equation [8], DNLS equation with cubic nonlinearity [9], and Klein-Gordon chain [10]. More recently, multibreathers have been predicted theoretically in * jtchinang@gmail.com † abtogueu@yahoo.fr ‡ Corresponding author: ctchawa@yahoo.fr realistic systems [11] and observed experimentally [12]. In spite the fact that multihump soliton have been observed in saturable dispersive nonlinear medium [13], their study is not yet done in purely discrete saturable nonlinear equation.…”