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Abstract In this paper, we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schrodinger equation driven by the subLaplacian dispersion operators (… Click to show full abstract
Abstract In this paper, we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schrodinger 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.
Journal Title: Physica D: Nonlinear Phenomena
Year Published: 2020
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