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 Gérard et al (A two soliton with transient turbulent regime for the one dimensional cubic half wave, 2018) for the critical case \(s=1\), but with a completely different asymptotic profile when the mass vanishes.
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Acknowledgements
Both authors are supported by the ERC-2014-CoG 646650 SingWave. P.R. would like to thank A. Soffer for stimulating discussions about this work and the Central China Normal University, Wuhan, where part of this work was done.
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Communicated by M. Struwe.
