Regular Article

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

¹ Laboratory of Advanced Microsystems Engineering, Department of Computer Science and Engineering, University of Quebec at Outaouais, 101 St-Jean-Bosco, Succursale Hull, Gatineau (PQ) J8Y 3G5, Canada
² Laboratory of Condensed Matter Theory and Materials Computation, Institute of Physics, Chinese Academy of Sciences, No. 8 South-Three Street, ZhongGuanCun, Beijing 100190, P.R. China

^a e-mail: kengem01@uqo.ca

Received: 10 April 2019
Received in final form: 12 August 2019
Published online: 15 October 2019

Abstract

Based on a modified one-dimensional Noguchi electrical transmission network containing a linear dispersive element C_S 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 C_s). 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 C_S 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 C_S 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 C_S, 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.