Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

Abstract

We study the propagation of voltage in a model of the conventional right-handed transmission line with a nonlinear symmetric capacitor. Applying the quasidiscrete approximation to the nonlinear voltage equation of the line, we derive a nonlinear Schrödinger equation and find the bright and dark solutions which are used as the initial condition for the integration of the nonlinear lattice model. The full integration of the lattice shows the propagation of the nonlinear voltage on the right-hand side and its robustness in time. The density energy of the lattice at each time has a node around which bright voltage is localized while in the case of dark voltage, it has a node where it seems to drop to zero at the soliton center. The plane phases allow proposing the characteristic of bright and dark solitons around the zero voltage.