Nonlinear excitations in a continuous bi-inductance electrical line

The dynamics of nonlinear excitations in an electrical bi-inductance transmission line are examined by means of the multiple scales method. In the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, we consider modulated waves and show that their propagation in the network is governed by a nonlinear Schrodinger equation instead of a Korteweg-de Vries equation. We have also established the existence of two frequency modes and study separately the wave dynamics in each mode. It appears from our investigations that the continuous bi-inductance electrical line supports a dark soliton in the low frequency mode and only a bright soliton in the high frequency mode. The study of the network properties has revealed that a nonlinear bi-inductance electrical transmission line can be considered as a superposition of two independent nonlinear mono-inductance transmission lines with different inductances.