Failure of scattering to standing waves for a Schr\"{o}dinger equation with long-range nonlinearity on star graph
Analysis of PDEs
2019-09-26 v1
Abstract
We consider the Schr\"{o}dinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, , or 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 Schr\"{o}dinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.
Keywords
Cite
@article{arxiv.1909.11332,
title = {Failure of scattering to standing waves for a Schr\"{o}dinger equation with long-range nonlinearity on star graph},
author = {Kazuki Aoki and Takahisa Inui and Haruya Mizutani},
journal= {arXiv preprint arXiv:1909.11332},
year = {2019}
}