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Mobility and reactivity of discrete breathers. (English) Zbl 1030.34501

Summary: Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in time. In some cases, there are exact mobile breather solutions (found numerically), but these solutions have an infinitely extended tail which shows that the breather motion is nonradiative only when it moves (in equilibrium) with a particular phonon field.
More generally, at any instability threshold, there is a marginal mode. There are situations where excitations by marginal modes produce new type of behaviors such as the fission of a breather. We may also have fusion. This approach suggests that breathers (which can be viewed as clusters of phonons) may react by themselves or with each other as well as in chemistry with atoms and molecules, or in nuclear physics with nuclei.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37K60 Lattice dynamics; integrable lattice equations
70K99 Nonlinear dynamics in mechanics
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