Spontaneous formation and resonant scattering of soliton molecules

We investigate spontaneous soliton molecule formation and molecule scattering by potential barriers. It is found that a stable two-soliton molecule forms only if the initial separation between the two solitons belongs to stability domains. The stability domains turn out to be finite disconnected regions embedded in a continuum for unstable molecules with sharp transitions from the stable to the unstable regimes. Similar behaviour is obtained upon scattering a soliton molecule by a potential barrier. Soliton molecules preserve their integrity after scattering if the barrier's height and the molecule's initial speed belong to some stability domains. The calculation is performed using a variational approach and the results were verified with direct numerical simulations of the relevant Gross-Pitaevskii equation. A simple model that qualitatively explains these results is presented.