Blow-up and strong instability of standing waves for the NLS-δ equation on a star graph. (July 2020) - Goloshchapova, Nataliia; Ohta, Masahito
Abstract: We study strong instability (by blow-up) of the standing waves for the nonlinear Schrödinger equation with δ -interaction on a star graph Γ . The key ingredient is a novel variational technique applied to the standing wave solutions being minimizers of a specific variational problem. We also show well-posedness of the corresponding Cauchy problem in the domain of the self-adjoint operator which defines δ -interaction. This permits to prove virial identity for the H 1 -solutions to the Cauchy problem. We also prove certain strong instability results for the standing waves of the NLS- δ ′ equation on the line.