Abstract:
This paper provides an overview of studies on nonlinear supratransmission and related phenomena. This effect consists
in the transfer of energy at frequencies not supported by the systems under consideration. The supratransmission does not
depend on the integrability of the system, it is resistant to damping and various classes of boundary conditions. In addition,
a nonlinear discrete medium, under certain general conditions imposed on the structure, can create instability due to external
periodic influence. This instability is the generative process underlying the nonlinear supratransmission. This is possible when
the system supports nonlinear modes of various nature, in particular, discrete breathers. Then the energy penetrates into the
system as soon as the amplitude of the external harmonic excitation exceeds the maximum amplitude of the static breather
of the same frequency.
The effect of nonlinear supratransmission is an important property of many discrete structures. A necessary condition
for its existence is the discreteness and nonlinearity of the medium. Its manifestation in systems of various nature speaks
of its fundamentality and significance. This review considers the main works that touch upon the issue of nonlinear
supratransmission in various systems, mainly model ones.
Many teams of authors are studying this effect. First of all, these are models described by discrete equations, including
sin-Gordon and the discrete Schrödinger equation. At the same time, the effect is not exclusively model and manifests itself in
full-scale experiments in electrical circuits, in nonlinear chains of oscillators, as well as in metastable modular metastructures.
There is a gradual complication of models, which leads to a deeper understanding of the phenomenon of supratransmission,
and the transition to disordered structures and those with elements of chaos structures allows us to talk about a more
subtle manifestation of this effect. Numerical asymptotic approaches make it possible to study nonlinear supratransmission
in complex nonintegrable systems. The complication of all kinds of oscillators, both physical and electrical, is relevant for
various real devices based on such systems, in particular, in the field of nano-objects and energy transport in them through the
considered effect. Such systems include molecular and crystalline clusters and nanodevices. In the conclusion of the paper,
the main trends in the research of nonlinear supratransmission are given.
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