Momentum-mass normalized dark-bright solitons to one dimensional Gross-Pitaevskii systems

Abstract: We rigorously establish the existence of dark-bright solitons as traveling wave solutions to a one dimensional defocusing Gross-Pitaevskii system, a widely used model for describing mixtures of Bose-Einstein condensates and nonlinear optical systems. These solitons are shown to exhibit symmetry and radial monotonicity in modulus, and to propagate at subsonic speed. Our method relies on minimizing an energy functional subject to two constraints: the mass of the bright component and a modified momentum of the dark component. The compactness of minimizing sequences is obtained via a concentration-compactness argument, which requires some novel estimates based on symmetric decreasing rearrangements.