On the linear wave regime of the Gross-Pitaevskii equation

Details On the linear wave regime of the Gross-Pitaevskii equation On the linear wave regime of the Gross-Pitaevskii equation

2008-09-22

arxiv.org/abs/0809.3512v2

Mathematics

Analysis of PDEs

Scientific paper

We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occurence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.

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