Abstract
We investigate analytically the dynamics of modulated waves in a nonlinear LC transmission line with dissipative elements. The damped nonlinear Schrödinger equation governing slowly modulated wave propagation is derived. Considering modulated plane wave propagating in the line, we establish their criteria of instability and show that, in the case of weak dissipation, there are no significant changes for the bandwidth frequency where the network may exhibit modulational instability (MI). However, dissipative losses constitute a great limiting factor to the experimental observation of the MI phenomenon. We show that the amplitude decreases, the width increases while the velocity remains constant when the soliton propagates along the dissipative network.
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