Coupled matter-wave solitons on oscillating reflectors under the effects of gravity

We consider coupled matter-waves solitons in Bose-Einstein condensates and study the dynamics under the combined effects of gravity and reflecting potential. The dynamics of matter-wave near a reflector oscillating periodically with time generates the dynamics of a special kind of localized structure called oscillon. We derive a mechanical model for the coupled oscillon dynamics. We pay special attention to the inter-component interaction and see that effective potential depends on the type (repulsive/attractive) and strength of interaction. We find that the inter-component interaction affects the frequency of oscillation and introduces an initial phase-shift between the reflector and the oscillon. This phase-shift, in addition to instantaneous phase change due to the oscillation of the reflector, results in interesting dynamics. The coupled oscillon is found to execute quasi-periodic and chaotic dynamics for both attractive and repulsive inter-component interactions. We analyze the maximum value of Lyapunov exponents and show that the dynamical response of the coupled oscillon depends on the ratio of the center of mass position and their separation.