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Logarithmic Gross-Pitaevskii equation

Abstract : We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions. We then characterize the solitary and travelling waves in the one dimensional case.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03790977
Contributor : Rémi Carles Connect in order to contact the contributor
Submitted on : Wednesday, September 28, 2022 - 7:03:58 PM
Last modification on : Friday, September 30, 2022 - 4:02:43 AM

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  • HAL Id : hal-03790977, version 1
  • ARXIV : 2209.14621

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Rémi Carles, Guillaume Ferriere. Logarithmic Gross-Pitaevskii equation. 2022. ⟨hal-03790977⟩

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