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The role of the collective excitations as well as the free expansion dynamicsprovide a key diagnostic tools for trapped Bose-Einstein condensations. Basedon such dynamics we proposed to study the relativistic version of them in thecontext of a macroscopic occupation of the ground-state for spin-0 particles.Therefore we used the Higgs model where the external trap is introduced by anon-minimal coupling. Along with variational method, we obtained a nonlinearcoupling between dipolar and monopolar modes. Furthermore, the free expansionis no longer ballistic reaching a relativistic confinement.

Dynamics of the relativistic Gross-Pitaevskii equation with harmonic potential: Following the variational approach