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math.AP2024
On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D
Nabile Boussaïd, Andrew Comech, Niranjana Kulkarni
For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the i…
math.SP2024
Virtual levels, virtual states, and the limiting absorption principle for higher order differential operators in 1D
Andrew Comech, Hatice Pekmez
We consider the resolvent estimates and properties of virtual states of the higher order derivatives in one dimension, focusing on Schroedinger-type operators of degree (the…
math.AP2024
Virtual levels and virtual states of linear operators in Banach spaces. Applications to Schroedinger operators
Nabile Boussaid, Andrew Comech
We develop a general approach to virtual levels in Banach spaces. We show that virtual levels admit several characterizations which are essentially equivalent: (1) there are corres…