Compact-like pulses along a low-pass reaction–diffusion electrical network with second-neighbor interactions effects

Abstract

This paper analytically and numerically explores the effects of second-neighbor interactions on the propagation and on the compact parameters of a compact-like wave packet in a low-pass reaction–diffusion electrical transmission line with the intersite circuit elements acting as nonlinear resistances. For the small amplitude signals in the network, the model equations are derived using Kirchhoff laws, which are eventually transformed to a family of nonlinear Burgers equation via the continuum limit approximations. Cusp, peak and compact-like solitary wave solutions of the equation have been derived, depending on the sign of the product of the nonlinearity coefficients. The width is related to the coefficients of the nonlinear dispersive terms and independent of its wave amplitude. The second-neighbor couplings generally well influence the wave width, increase the bandwidth frequencies of the network, modify group velocity and energy transmission of the wave during propagation. It is obvious that the second-neighbor interactions may equally trigger the simultaneous propagation of two nonlinear waves with the same frequency and minimize the dissipative effects on the compact-like pulse voltage signal of the nonlinear electrical transmission line. Our proposed electrical circuit has potential applications in high-speed electronic devices.