Management of modulated wave solitons in a two-dimensional nonlinear transmission network

Abstract

Based on a modified one-dimensional Noguchi electrical transmission network containing a linear dispersive element CS with a voltage source and a one-dimensional series capacitor transmission network, we build a two-dimensional nonlinear discrete electrical network which allow the wave propagation in both the longitudinal and the transverse direction. These transmission lines are coupled to one another in the transverse (longitudinal) direction by a linear capacitor C2 (a linear inductor L1 in parallel with the linear capacitance Cs). The linear dispersion relation of the network system is derived and the effects of the transverse coupling element C2 on the linear waves are established. Using the continuum limit approximation and assuming that the perturbation voltage is small enough compared with the equilibrium value, we show that the dynamics of small-amplitude pulses in the network can be governed by a two-dimensional modified Zakharov–Kuznetsov (ZK) equation with a voltage source term. Analyzing the wave propagation in a reduced direction, we show that a best choice of the coupling capacitance C2 and the linear dispersive element CS can lead to the propagation at the same frequency of two distinct waves propagating in different reduced propagation directions. The transverse stability of plane solitary waves is investigated and the effects of the dispersive element CS on the transverse instability are presented. Through the analytical exact bright solitary wave solution of the derived ZK equation, we investigate analytically the effects of the linear dispersive element CS, the effects of the management parameter, and the effects of the reduce propagation direction on the characteristic parameters (amplitude, width, and velocity) of bright solitary waves propagating through our network system. We find that the management parameter of the ZK equation can be used to manipulate the motion of pulse voltages through the network system.