Author: A Alvarez (pdf poster)
With J Cuevas, FR Romero and PG Kevrekidis.

We numerically investigate the existence, stability, dynamics and interactions of single and multiple dark-bright solitons (not only between them, but also with dark solitons) in the setting of nonlinear dynamical lattices. The discrete content enabled a number of interesting variants to the previously studied continuous setting. Some of these variants could be anticipated on the basis of analogous studies of dark solitons, e.g., the dark-bright single solitons could be stable only up to a critical coupling (although ¯nite-size e®ects could provide additional stabilization). The same thing would be true for pairs of dark-bright and dark solitons. The collisions of the latter pairs indicate the repulsive interaction between the dark-bright and the dark states. On the other hand, a number of interesting novel features was revealed. Relevant examples include the generic instability of the dark-bright for a su±ciently strong bright component, the generic instability of out-of-phase two-DB soliton pairs, and the generic stability (for small coupling and small enough bright component) of in-phase two-DB soliton pairs. Discreteness was also found to play a signi¯cant role in a®ecting collisions for \intermediate" coupling strengths (not too small, so that the excitations would get pinned, nor too large so that they would interact in a quasi-continuum way). There, its potential combination with the dynamical instability e.g. of stationary dark solitons could yield a variety of interesting collisional outcomes.

NDS2011: Nonlinear Dynamics of Electronic Systems, Kolkata, India, March 8-11, 2011. Poster  by A Alvarez.