Analytical studies of soliton pulses along two-dimensional coupled nonlinear transmission lines

A nonlinear network with many coupled nonlinear LC dispersive transmission lines is considered, each line of the network containing a finite number of cells. In the semi-discrete limit, we apply the reductive perturbation method and show that the wave propagation along the network is governed by a two-dimensional nonlinear partial differential equation (2-D NPDE) of Schrödinger type. Two regimes of wave propagation, the high-frequency and the low-frequency are detected. By the means of exact soliton solution of the 2-D NPDE, we investigate analytically the soliton pulse propagation in the network. Our results show that the network under consideration supports the propagation of kink and dark solitons.