The existence of compacton matter waves in binary mixtures of quasi one-dimensional BoseEinstein condensates in deep optical lattices and in the presence of nonlinearity management, is first demonstrated. For this, we derive an averaged vector discrete nonlinear Schrödinger equation (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system and their dependence on the inter-and intra-species scattering lengths, investigated. We show that under proper management conditions, compactons can be very robust excitations that can emerge spontaneously from generic initial conditions. A possible experimental setting for compacton observation is also discussed.
Abstract. Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) in the presence of periodic time modulations of the inter-species scattering length, are investigated. We adopt a mean field description and use the tight binding approximation and the averaging method to derive averaged model equations in the form of two coupled discrete nonlinear Schrödinger equations (DNLSE) with tunneling constants that nonlinearly depend on the inter-species coupling. We show that for strong and rapid modulations of the interspecies scattering length, the averaged system admits exact compacton solutions, e.g. solutions that have no tails and are fully localized on a compact which are achieved when the densities at the compact edges are in correspondence with zeros of the Bessel function (zero tunneling condition). Deviations from exact conditions give rise to the formation of quasi-compactons, e.g. non exact excitations which look as compactons for any practical purpose, for which the zero tunneling condition is achieved dynamically thanks to an effective nonlinear dispersive coupling induced by the scattering length modulation. Stability properties of compactons and quasi-compactons are investigated by linear analysis and by numerical integrations of the averaged system, respectively, and results compared with those from the original (unaveraged) system. In particular, the occurrence od delocalizing transitions with existence of thresholds in the mean inter-species scattering length is explicitly demonstrated. Under proper management conditions, stationary compactons and quasi-compactons are quite stable and robust excitations that can survive on very long time scale. A parameter design and a possible experimental setting for observation of these excitations are briefly discussed.
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