Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations
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- Yakine Bahri
- Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, Victoria, BC V8P 5C2, Canada
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- Slim Ibrahim
- Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, Victoria, BC V8P 5C2, Canada
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- Hiroaki Kikuchi
- Department of Mathematics, Tsuda University, 2-1-1 Tsuda-machi, Kodaira-shi, Tokyo 187-8577, Japan
抄録
<jats:p> In this paper, we study solitary wave solutions of the Cauchy problem for Half-wave-Schrödinger equation in the plane. First, we show the existence and the orbital stability of the ground states. Second, we prove that given any speed [Formula: see text], traveling wave solutions exist and converge to the zero wave as the velocity tends to [Formula: see text]. Finally, we solve the Cauchy problem for initial data in [Formula: see text], with [Formula: see text]. The critical case [Formula: see text] still stands as an interesting open problem. </jats:p>
収録刊行物
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- Communications in Contemporary Mathematics
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Communications in Contemporary Mathematics 23 (05), 2050058-, 2020-09-11
World Scientific Pub Co Pte Lt
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詳細情報 詳細情報について
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- CRID
- 1360290617474214784
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- ISSN
- 17936683
- 02191997
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- データソース種別
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- Crossref
- KAKEN