Dynamics of modulated waves in a lossy modified Noguchi electrical transmission line

We study analytically the dynamics of modulated waves in a dissipative modified Noguchi nonlinear electrical network. In the continuum limit, we use the reductive perturbation method in the semidiscrete limit to establish that the propagation of modulated waves in the network is governed by a dissipative nonlinear Schrödinger (NLS) equation. Motivated with a solitary wave type of solution to the NLS equation, we use both the direct method and the Weierstrass's elliptic function method to present classes of bright, kink, and dark solitary wavelike solutions to the dissipative NLS equation of the network. Through the exact solitary wavelike solutions to the dissipative NLS equation, we investigate the effects of the dissipative elements of the network on wave propagation. We show that the wave amplitude decreases and its width increases when the dissipative element of the network increases. It has been also found that the dissipative element of the network can be used to manipulate the motion of solitary waves through the network. This work presents a good analytical approach of investigating the propagation of solitary waves through discrete electrical transmission lines and is very important for studying modulational instability.