Mobility and reactivity of discrete breathers

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. © 1998 Elsevier Science B.V. 1. Breathers by the principle of anticontinuity: Brief review of current developments The concept of nonlinear self-localization which is now emerging as ubiquitous in many highly non-linear models has an old historical origin. Although exact localized and time periodic solutions were al