Tackling the Gross-Pitaevskii energy functional with the Sobolev gradient - Analytical and numerical results

In this contribution, we prove the global existence and uniqueness of a trajectory that globally converges to the minimizer of the Gross-Pitaevskii energy functional for a large class of external potentials. Using the method of Sobolev gradients, we can provide an explicit construction of this minimizing sequence. Based upon this theoretical framework we numerically apply these results to a specific realization of the external potential and illustrate the main benefits of the method of Sobolev gradients, which are high numerical stability and rapid convergence toward the minimizer.

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