Résumé
We study the stability of a stationary discrete breather (DB) on a nonlinear
trimer in the framework of the discrete nonlinear Schrödinger equation
(DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein
condensates in leaking optical lattices, collisions between a DB and a lattice
excitation, e.g. a moving breather (MB) or phonon, were studied. These
collisions lead to the transmission of a fraction of the incident (atomic) norm
of the MB through the DB, while the DB can be shifted in the direction of the
incident lattice excitation. Here we show that there exists a total energy
threshold of the trimer, above which the lattice excitation can trigger the
destabilization of the DB and that this is the mechanism leading to the
movement of the DB. Furthermore, we give an analytic estimate of upper bound to
the norm that is transmitted through the DB. Our analysis explains the results
of the earlier numerical studies and may help to clarify functional operations
with BECs in optical lattices such as blocking and filtering coherent (atomic)
beams.