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.

The dynamics of two electrical pulses forming a boundstate, propagating along two nonlinear transmission lines weakly coupled by linear capacitors shunted with linear resistances, is considered from both analytical and numerical standpoints. The study rests on an analysis of time series of the amplitudes and phases of the two interacting electrical pulses, within the framework of the variational theory based on exact one-soliton solution to the Korteweg-de Vries equation. In the regime where the two pulses propagate at nearly equal velocities, their relative amplitude/phase evolutions can result in periodic quasi-harmonic oscillations so-called leapfrogging motion. In this specific regime of motion, it is found that besides the expected damping effect on the soliton amplitudes, the resistance can also sustain their leapfrogging motion. Analytical expression of the leapfrogging frequency is derived, providing a better understanding of the competing effects of the coupling capacitor and the resistive shunt on the leapfrogging motion. Leapfrogging motions of co-propagating pulses in electrical networks can be very useful in high-intensity signal transmissions involving least energy cost for the propagating signals.