Characterization of leapfrogging solitary waves in coupled nonlinear transmission lines

Abstract

Leapfrogging solitary waves are characterized in two capacitively coupled transmission lines that are periodically loaded with Schottky varactors, called coupled nonlinear transmission lines (NLTLs). The coupling implies that a nonlinear solitary wave moving on one of the lines is bounded with the wave moving on the other line, which results in the periodic amplitude/phase oscillation called leapfrogging. In this study, we clarify how the leapfrogging frequency depends on the physical parameters of coupled NLTLs using a numerical model validated through measuring test lines and demonstrate the relaxation of leapfrogging. In addition, coupled Korteweg-de Vries equations are derived by applying the reductive perturbation method to the transmission equations of coupled NLTLs. Using perturbation theory based on the inverse scattering transform, a closed-form expression of leapfrogging frequency is obtained and the parameter values that simulate the properties well are examined. Engineering applications based on leapfrogging are finally discussed.