We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap exhibiting superfluid (SF) and Mott-insulator shell structures. An earlier study [K. V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A82, 033618 (2010)PLRAAN1050-294710.1103/PhysRevA.82.033618] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons. We also reveal another type of phase-imprinted soliton, the hybrid soliton. In a harmonically trapped system, solitonic excitations created at the SF core cannot penetrate the outer SF shell. This repulsion at the surface of the outer SF shell can be counteracted by imposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of impedance matching of excitations in Bose-Einstein condensates in terms of the effective chemical potentials or local particle numbers in the shell, and analogous results can be observed in sound waves created by a local single-shot pulse potential.
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