2019/09/25 by Kazuki Aoki, Aoki, Kazuki, Takahisa Inui +3
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1909.11332
We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, δ, or δ' boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi, who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.