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Asymptotic behavior for
the long-range nonlinear Schrödinger equation on the star
graph with the Kirchhoff boundary condition
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani and Kota Uriya |
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Vol. 4 (2022), No. 2, 287–311
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DOI: 10.2140/paa.2022.4.287
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Abstract |
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We consider the cubic nonlinear Schrödinger 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 Schrödinger equation with power-type long-range nonlinearities. These results are extensions of the results for the nonlinear Schrödinger equation on the one-dimensional Euclidean space. |
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Keywords
Schrödinger equation, star graph, long-range nonlinearity,
modified scattering, failure of scattering
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Mathematical Subject Classification
Primary: 35B40, 35Q55
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Milestones
Received: 31 March 2021
Accepted: 11 January 2022
Published: 16 October 2022
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Authors |
| Kazuki Aoki | |
| Department of Mathematics, Graduate
School of Science Osaka University Toyonaka-shi Japan |
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| Takahisa Inui | |
| Department of Mathematics, Graduate
School of Science Osaka University Toyonaka-shi Japan |
Department of Mathematics University of British Columbia Vancouver Canada |
| Hayato Miyazaki | |
| Teacher Training Courses, Faculty of
Education Kagawa University Takamatsu-shi Japan |
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| Haruya Mizutani | |
| Department of Mathematics, Graduate
School of Science Osaka University Toyonaka-shi Japan |
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| Kota Uriya | |
| Department of Applied Mathematics,
Faculty of Science Okayama University of Science Okayama-shi Japan |
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