Dynamics of nonlinear waves in a low-pass reaction diffusion electrical network and some exact and implicit Modulated compact solutions

In this paper, we analytically investigate the dynamic behavior of the extended nonlinear Schrödinger (ENLS) equation. This equation describes the propagation of the modulated waves in the network characterized by the nonlinear resistance (NLR) by using the rotative waves approximation. Based on the theory of singular systems and investigating the dynamical behavior of the network, we obtain bifurcations of the phase portraits of the system under different parameter conditions. The result of this qualitative investigation indicates the existence of the nonlinear localized waves with linear phase shift, such as bright pulses, peak pulses, dark pulses, compact dark and compact pulses solitary waves. These nonlinear localized waves can be used in signal processing, electronic devices, and ultra-fast metrology. We derive possible exact explicit and implicit solutions propagating in the nonlinear low-pass electrical transmission line with nonlinear dispersion depending on the frequency range of the chosen carrier wave, for physically realistic parameters.