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Inelastic collisions occur in Bose-Einstein condensates, in some cases,producing particle loss in the system. Nevertheless, these processes have notbeen studied in the case when particles do not escape the trap. We show thatsuch inelastic processes are relevant in quantum properties of the system suchas the evolution of the relative population, the self trapping effect and theprobability distribution of particles. Moreover, including inelastic terms inthe model of the two-mode condensate allows for an exact analytical solution.Using this solution, we show that collisions favor the generation ofentanglement between the modes of the condensate as long as the collision ratedoes not exceed the natural frequency of the system

Mode-exchange collisions in an exactly solvable two-mode Bose-Einstein condensate