On the standing waves of the NLS-log equation with a point interaction on a star graph

摘要

We study the nonlinear Schrodinger equation with logarithmic nonlinearity on a star graph g. At the vertex an interaction occurs described by a boundary condition of delta type with strength alpha is an element of R. We investigate the orbital stability and the spectral instability of the standing wave solutions e(i omega t)Phi(x) to the equation when the profile Phi(x) has mixed structure (i.e. has bumps and tails). In our approach we essentially use the extension theory of symmetric operators by Krein-von Neumann, and the analytic perturbations theory. (C) 2018 Elsevier Inc. All rights reserved.