Dynamics of spatiotemporal modulated damped signals in a nonlinear RLC transmission network

The dynamics of spatiotemporal modulated damped signals in a nonlinear LC transmission network with dissipative elements are investigated analytically. The complex cubic Ginzburg–Landau (GL) equation governing slowly modulated wave propagation is presented. Considering linear wave propagating in the network, we derive in terms of the propagating frequency the spatial decreasing rate (linear dissipation parameter) and show that its must important contribution comes from the dissipative element of the shunt branch. The modulational instability (MI) criterion of modulated Stokes wave propagating in the network is investigated and the analytical expression of the MI growth rate is derived; we show that in the case of weak dissipation, there are no significant changes for the bandwidth frequency where the network may exhibit MI. Exact and approximative envelope soliton-like solutions of the derived GL equation are presented and used to investigate the dynamics of spatiotemporal modulated damped signals along the network. We show that the solution parameters can be used for managing the evolution of the envelope soliton signals along the network. Our investigation shows that the amplitude decays in both space (cell number n) and time t, while the velocity remains constant when the envelope soliton signal propagates along the dissipative network.