Bistability in the sine-Gordon equation: The ideal switch

Abstract

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an ideal switch by reaching a transmissive regime with vanishing driving amplitude.

The affective factors on the uncertainty in the collisions of the soliton solutions of the double field sine-Gordon system

“…However, inserting the little disturbed non-moving H-soliton (21), as an ansatz, into the non-linear differential equations (8) and (9) and expanding to the first order in Ψ and Φ, we obtain two independent eigenvalue equations for Ψ and Φ respectively, which look like the Schrödinger equation:…”

“…They are localized objects and do not disperse while propagating in the medium. The integrable SG system has been considered in recent investigations, it has various applications in many branches of physics [5,[9][10][11][12][13]. Because of their wave nature, they do tunnel a barrier in certain cases, although this tunnelling is different from the well-known quantum version [5,14].…”

Frequency divider by underdamped Josephson transmission line

“…One can quote the perturbation analysis [6] and modulation instability studies [7] of a e-mail: khomeriki@hotmail.com the process, theoretical [8,9] and experimental [10,11] investigations of the resonances between fluxons and linear plasma oscillations, fluxon dynamics studies in case of coupled JTL-s [12,13], fluxon induced directed transport under homogeneous ac driving with broken time symmetry [14] and many other interesting phenomena. At the same time, much less studies have been devoted to the dynamics of nonlinear excitations under the local (boundary) driving: In this connection one should mention the investigation of hysteretic regimes appearing due to the phase locking effect between the boundary driving and breather type localizations [15][16][17] (where the breathing frequency coincides with the driver frequency [18][19][20]) or, on the other hand, boundary driving can maintain stationary motion of the fluxon which creates a new frequency in the system being an odd fraction of the driving frequency [21][22][23]. However, in all of the previous studies the driving is applied from the both ends and in order to observe the effect one has to measure the averaged quantities or some emitted radiation.…”

On the Generation of Localized Nonlinear Modes in a Linear Array of Anharmonic Oscillators

“…The theory for harmonic chains is governed by systems of equations of the Klein-Gordon type 17 that may be solved numerically in many instances, 18 and the investigation has shown that many of such systems present the nonlinear phenomenon of transmission of energy in the forbidden band-gap. [19][20][21] Moreover, it was recently discovered that one of the models studied by Fermi, Pasta, Ulam, and Tsingou has the capability of transmitting energy in the forbidden band-gap. 22 It was recently shown that harmonic chains of oscillators are capable to transmit energy above a critical input-amplitude value called the supratransmission threshold in both the (1 + 1)-dimensional 23 and the (2 + 1)-dimensional 24 scenarios.…”