ON SMALL TRAVELING WAVES TO THE MASS CRITICAL FRACTIONAL NLS

Ivan Naumkin (1) , Pierre Raphaël (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Université de Nice

We consider the mass critical fractional (NLS) i∂tu − |D| s u + u |u| 2s = 0, x ∈ R, 1 < s < 2. 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 [6] for the critical case s = 1, but with a completely different asymptotic profile when the mass vanishes.

Domaines: Equations aux dérivées partielles [math.AP]

Ivan Naumkin, Pierre Raphaël. ON SMALL TRAVELING WAVES TO THE MASS CRITICAL FRACTIONAL NLS. 2018. ⟨hal-01808636⟩