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arXiv · 1712.04484

On small travelling waves to the mass critical fractional NLS

Ivan Naumkin·Pierre Raphaël
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Abstract

We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a situation similar to the one discovered in [Gerard P.; Lenzmann E.; Pocovnicu O.; Rapha\"el, P., A two soliton with transient turbulent regime for the one dimensional cubic half wave, submitted] for the critical case s = 1, but with a completely different asymptotic profile when the mass vanishes.

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Ivan Naumkin, Pierre Raphaël. 2017-12-12. On small travelling waves to the mass critical fractional NLS. https://arxiv.org/abs/1712.04484

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