Abstract:We consider an inner problem for whispering gallery highfrequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schrödinger equation on a halfline with a potential linear in both space and time appears fundamental for describing transitions from modal to scattered asymptotic patterns, and despite having been intensively studied over several decades remains largely unsolved. We prove that the solution past the inflection point has a "searchlight" asymptotics cor… Show more
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