Higher Order Solitons in an Electrical Lattice

Abstract

Dynamics of modulated waves in a nonlinear electrical bi-inductance line are theoretically examined by the means of a perturbation method. It has been recently established that in such lines, modulations of weakly nonlinear dispersive waves are described by the complex Ginzburg–Landau equation (CGLE) for wavenumbers k larger than the critical values k c . Presently, we assume that in the vicinity of k c , the CGLE is invalid and the associated instability criterion is useless. Considering a semi discrete approximation using an appropriate decoupling ansatz for the voltage of the two different cells, we demonstrated that in such regime, wave evolutions are governed by a modified form of the CGLE that involves higher-orders nonlinearities. The associated generalized modulation instability criterion is obtained and corresponding higher order soliton solutions are constructed.