Dark-bright solitons to one-dimensional Gross-Pitaevskii systems

by Salvador López Martinez

Tuesday Jun 3, 2025, 11:15 AM → 12:15 PM Europe/Paris

Salle J. Cavailles (IMT)

Solitons are localized structures that propagate at constant speed without changing shape. These structures typically arise in physical systems governed by coupled Gross-Pitaevskii equations, such as mixtures of Bose-Einstein condensates (BECs) and multimode nonlinear optics. Solitons are classified as dark or bright, depending on whether the density is a positive constant or zero at infinity, and emerge under repulsive (defocusing) or attractive (focusing) interactions, respectively. Experimental and numerical studies confirm the existence of stable dark-bright solitons, even when self-defocusing interactions are present in the bright component. In this talk, we will present recent analytical results that rigorously validate this phenomenon. Specifically, we will show that symmetric and radially monotone (in modulus) dark-bright solitons can be derived as energy minimizers subject to a momentum-mass constraint.