Variational methods reveal global existence and orbital stability in two-component bose-einstein condensates, suggesting new insights into their dynamics.
We consider the critical coupled nonlinear Gross-Pitaevskii equations with attractive interactions in harmonic potentials, modeling two-component Bose-Einstein condensates (BEC). By using the variational characteristic of the classic nonlinear scalar field equation and the Hamilton conservations, we determine the sharp threshold for global existence of the Cauchy problem on mass. Based on this threshold, we prove the existence and orbital stability of the ground states.
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Zhou et al. (2025) studied this question.
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