Asymptotic behavior for the long-range nonlinear Schr\"odinger equation on star graph with the Kirchhoff boundary condition
Analysis of PDEs
2022-10-19 v2
Abstract
We consider the cubic nonlinear Schr\"{o}dinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initial value problem. Moreover, we also consider the failure of scattering for the Schr\"{o}dinger equation with power-type long-range nonlinearities. These results are extension of the results for NLS on the one dimensional Euclidean space.
Keywords
Cite
@article{arxiv.2006.13490,
title = {Asymptotic behavior for the long-range nonlinear Schr\"odinger equation on star graph with the Kirchhoff boundary condition},
author = {Kazuki Aoki and Takahisa Inui and Hayato Miyazaki and Haruya Mizutani and Kota Uriya},
journal= {arXiv preprint arXiv:2006.13490},
year = {2022}
}