Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies

Gustafson, Stephen; Inui, Takahisa

doi:https://doi.org/10.1016/j.jde.2024.08.072

Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies

Gustafson, Stephen; Inui, Takahisa

Journal of Differential Equations, 2024, 412, 758-796

アクセス数:40件（2025-07-11 22:03 集計）

固定URL: https://hdl.handle.net/11094/98335

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タイトル	Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies
著者	著者名 Gustafson, Stephen
著者	NRID 1000070814648 1000070814648 researchmap permalink takahisa_inui takahisa_inui Scopus Author ID 56480025400 56480025400 著者名 Inui, Takahisa
キーワード等	Blow-up
	Even solutions
	Nonlinear Schrödinger equation
	Repulsive Dirac delta potential
	Scattering
内容	Gustafson S., Inui T. Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies. Journal of Differential Equations 412, 758 (2024); https://doi.org/10.1016/j.jde.2024.08.072.
抄録	We consider the L²-supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential in one dimensional space. In a previous work, we clarified the global dynamics of even solutions with the same action as the high-frequency ground state standing wave solutions. In that case, there are obvious non-scattering global solutions, i.e., the standing waves. In this paper, we show a scattering and blow-up dichotomy for threshold even solutions in the low-frequency case. We emphasize that this dichotomy still holds at the critical frequency between high and low.
出版者	Elsevier B.V.
収録物名	Journal of Differential Equations
巻(号)	412
ページ	758-796
刊行年月	2024-12-15
言語	英語
ハンドルURL	https://hdl.handle.net/11094/98335
PISSN	00220396
eISSN	10902732
関連情報 (isIdenticalTo)	DOI (出版社版) https://doi.org/10.1016/j.jde.2024.08.072
アクセス権	open access
権利情報	This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
出版タイプ	Version of Record
カテゴリ	学術雑誌論文 Journal Article

資源タイプ	学術雑誌論文
ローカル資源タイプ	学術雑誌論文
DCTERMS.bibliographicCitation	Journal of Differential Equations. 2024, 412, p. 758-796
DC.title	Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies
DC.creator	Gustafson, Stephen
DC.creator	Inui, Takahisa
DC.publisher	Elsevier B.V.
DC.language' scheme='DCTERMS.RFC1766	英語
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2024-12-15
DC.identifier	https://doi.org/10.1016/j.jde.2024.08.072
DC.subject	Blow-up
	Even solutions
	Nonlinear Schrödinger equation
	Repulsive Dirac delta potential
	Scattering
DC.description	Gustafson S., Inui T. Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies. Journal of Differential Equations 412, 758 (2024); https://doi.org/10.1016/j.jde.2024.08.072.
DCTERMS.abstract	We consider the L²-supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential in one dimensional space. In a previous work, we clarified the global dynamics of even solutions with the same action as the high-frequency ground state standing wave solutions. In that case, there are obvious non-scattering global solutions, i.e., the standing waves. In this paper, we show a scattering and blow-up dichotomy for threshold even solutions in the low-frequency case. We emphasize that this dichotomy still holds at the critical frequency between high and low.
DC.rights	This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
DC.format	98335
citation_title	Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies
citation_author	Gustafson, Stephen
citation_author	Inui, Takahisa
citation_publisher	Elsevier B.V.
citation_language	英語
citation_date	2024-12-15
citation_journal_title	Journal of Differential Equations
citation_volume	412
citation_firstpage	758
citation_lastpage	796
citation_doi	https://doi.org/10.1016/j.jde.2024.08.072
citation_public_url	https://hdl.handle.net/11094/98335

Scattering and blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies

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