Abstract
In this paper, we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schrödinger equation driven by the subLaplacian dispersion operators (−Δ)s,0<s≤1. We construct these waves and we establish sharp asymptotics, both at the singularity 0 and for large values. We show the non-degeneracy of these waves. Finally, we provide spectral and orbital stability classification, under slightly more restrictive assumptions.
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