Speaker: Magnus Johansson

Abstract: It is well known that diatomic anharmonic chains may sustain localized solutions with frequencies inside the gap of the linear wave spectrum. In the continuum limit, such solutions are called gap solitons and have been extensively analyzed earlier. Here, we take full account of the discreteness and investigate numerically the properties of 'gap breathers', which are the corresponding exact lattice solutions. Considering the case of a Klein-Gordon chain with hard (quartic) nonlinearity, there are two fundamental discrete solutions which both approach the gap soliton in the continuum limit; one spatially symmetric around a central heavy atom and another antisymmetric around a central light atom. Both solutions are continuable to the uncoupled (anticontinuous) limit, where the symmetric breather corresponds to a single-site vibration of a heavy atom and the antisymmetric breather to out-of-phase vibrations of two neighboring heavy atoms. Performing a linear stability analysis, we find the symmetric breather always to be stable and the antisymmetric breather unstable for weak inter-site coupling ('Peierls-Nabarro-type' instability), while for larger coupling the stability between the two breathers is generally inverted in some regime. Close to the  stability-inversion points, very good mobility is observed. There are also several other instability mechanisms that we describe (6 in total). One corresponds to a transition between continuum-like and discrete-like solutions, and can be determined from a Vakhitov-Kolokolov-type criterion (change of sign of the derivative of the energy-vs-frequency functional). The remaining 4 are oscillatory ('Krein') instabilities, some of them surviving also in the continuum limit. Several of these also result in breather motion.

MOBIL. Moving Breathers in Inhomogeneous Lattices. Workshop at Sevilla, 21-22 February 2003.