Influence of impurities on solitons in the nonlinear LC transmission line

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.

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.