Asymptotic behavior for the long-range nonlinear Schr\"odinger equation on star graph with the Kirchhoff boundary condition

Pure Appl. Analysis 4 (2022) 287-311 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...

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Bibliographic Details
Main Authors Aoki, Kazuki, Inui, Takahisa, Miyazaki, Hayato, Mizutani, Haruya, Uriya, Kota
Format Journal Article
LanguageEnglish
Published 24.06.2020
Subjects
Mathematics - Analysis of PDEs
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Summary:Pure Appl. Analysis 4 (2022) 287-311 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.
DOI:10.48550/arxiv.2006.13490