Observation Of Resonant Emission Of Solitions From Localized Waves

Solitons are a special kind of nonlinear localized waves,caused by a dynamic balance of nonlinear and dispersive effects in the medium.The soliton concept and the relavent theory are now firmly established since the first discovery of solitary waves by Scott Russel in the early 19th century,and many kinds of soliton phenomena have observed both in nature and in experiments.However,the problem regarding to the inner mechanism of soliton creations,which is not only fundamental to understanding occurring solitonic phenomena in nature and physical systems but also is highly relevant to engineering applications of solitons,is still unclear and yet to be further exploredBased on the approaches of resonant emission of solitons from impurity-induced localized waves proposed by our research group theoretically and a physical model designed recently by Wang,we build an experimental setup and first observe the resonant emission of solitons in an array of coupled pendulums driven at one end by a small transverse displacement signal.The experimental measurements show that the rate of emission of solitons highly depends on the driving parameters,here the driving amplitude and frequency.The rate of emission increases with the growth of driving amplitude,while decreases with the driving frequency away from the cutoff frequency.Further,the driving threshold,i.e.the minimal driving amplitude that is required for initiating the emission of solitons,increases as the driving frequency rises.All the experimental results are in accordance with the previous theoretical results of our research group,confirming that this new way of controlled creation of soliton is applicable and effective.The concept of locally resonant emission of solitons is widely applicable,not only in mechanical systems such as what we have investigated,but also in other systems like electrical circuit ones.In consideration of the advantages of measurement and replacement of devices in circuits,we have also investigated the emission of solitons in typical nonlinear LC circuits numerically.The impurities we concern are two different types,namely capacitance impurity and capacitance-inductance impurity.Our numerical simulations indicate that resonance of the impurity-induced local waves also leads to the radiation of electrical solitons,with a driving amplitude quite smaller than the threshold of other methods as predicted by Koon.