Nonlinear wave transmission in a two-dimensional nonlinear electric transmission network with dissipative elements

Abstract

A two-dimensional nonlinear discrete electric transmission network made of several well-known anharmonic modified Noguchi lines coupled transversely to one another with a linear inductor is considered and the dynamics of modulated waves are investigated. The linear analysis shows that increasing either the dispersive elements of the network, the coupling elements of the network, or the transverse wavenumber increases the propagating frequencies. Employing the reductive perturbation method, we establish that the dynamics of modulated waves in the network system are governed by a two-dimensional dissipative nonlinear Schrödinger (NLS) equation having, depending on both the longitudinal and transverse wavenumbers as well as on the network parameters, either the hyperbolic or the elliptic character. Through the derived dissipative NLS equation, the phenomenon of the baseband modulational instability (MI) of the electric system under consideration is investigated and the analytical expression for the baseband MI growth rate is presented. We show that the dispersive elements of the network system softens the baseband MI and enhances the baseband MI domain. Under the condition of the baseband MI, we find approximate modulated wave solutions of the governing equations which are then used for analytical investigation of the transmission of super rogue wave voltage, Peregrine soliton voltage, and bright solitary wave signals through the network system under consideration. The effects of the network and solution parameters such as the dispersive, coupling parameters, the carrier wavenumber, and the wavenumbers in both the longitudinal and transverse directions on the dissipative wave signals are presented.