Experimental observation of the generation of cutoff solitons in a discreteLCnonlinear electrical line

Abstract

We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact can be managed by a proper choice of the amplitude of the voltage excitation of the system.

The effect of nonlinear supratransmission in discrete structures: a review

“…Наиболее простыми в реализации и поддающимися простому моделированию являются электрические нелинейные системы. На возможность существования и перспективы проявления НСТ в таких системах обратил внимание целый ряд исследователей [Tao et al, 2012a;Tao et al, 2012b;Togueu Motcheyo et al, 2013;Kenmogne et al, 2015;Koon, Marquié, Dinda, 2014;Togueu Motcheyo, Tchawoua, Tchinang Tchameu, 2013].…”

“…Так, в работе [Koon, Marquié, Dinda, 2014] изучается 200-элементная электрическая линия, в ней осуществлена генерация солитонов и их распространения за счет формирования модуляционной неустойчивости на границах. Авторы отмечают, что полученным солитонам сильно мешает диссипация, возникающая из-за несовершенства компонентов электрической линии (индуктивностей).…”

Leapfrogging dynamics of interacting solitons in weakly coupled nonlinear transmission lines

“…(9), (10), (11), (12) and (13) into Eqs. (7) and (8), and keeping only terms of order 3 for which nonlinearity balances the dispersion, we obtain the following two coupled KdV equations at the third order in :…”

“…Nonlinear transmission lines (NLTLs) are dispersive media in which electric signals propagate in form of well-localized pulses [1][2][3][4][5][6][7][8][9][10][11][12][13], usually referred to as electrical solitons. Owing to their robustness that is their ability to cover long distances (thousands of kilometers) without change in profiles, electrical solitons have been actively investigated over the past fifty years starting from the pioneer model of Hirota and Suzuki [1,2,[14][15][16][17][18][19][20][21][22][23].…”