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Binary discrete nonlinear Schr\"odinger equation is used to describe dynamicsof two-species Bose-Einstein condensate loaded into an optical lattice. Linearinter-species coupling leads to Rabi transitions between the species. In theregime of strong nonlinearity, a wavepacket corresponding to condensateseparates into localized and ballistic fractions. Localized fraction ispredominantly formed by immiscible solitons consisted of only one species.Initial states without spatial separation of occupied sites expose formation ofimmiscible solitons after a strongly chaotic transient. We calculate thefinite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbertspace. Using the Lyapunov analysis supplemented by Monte-Carlo sampling, it isshown that appearance of immiscible solitons after the chaotic transientcorresponds to self-stabilization of the wavepacket. It is found that onset ofchaos is accompanied by fast variations of kinetic and interaction energies.Crossover to self-stabilization is accompanied by reduction of condensatedensity due to emittance of ballistically propagating waves. It turns out thatspatial separation of species should be a necessary condition for wavepacketstability in the presence of linear inter-species coupling.

Chaos-assisted formation of immiscible matter-wave solitons and self-stabilization in the binary discrete nonlinear Schr\"odinger equation