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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全 | |
| dc.contributor.author | Kuan-Ting Yeh | en |
| dc.contributor.author | 葉冠廷 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:42:48Z | - |
| dc.date.available | 2015-08-20 | |
| dc.date.available | 2021-05-14T17:42:48Z | - |
| dc.date.copyright | 2015-08-20 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-14 | |
| dc.identifier.citation | References
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[7] Bona J.L., Li, Y.A.: Decay and analyticity of solitary waves. J. Math. Pures Appl., 76(5):377– 430, 1997. [8] Chiron, D.: Travelling waves for the Gross-Pitaevskii equation in dimension larger than two. Nonlinear Anal., 58(1-2):175–204, 2004. [9] de Bouard, A., and Saut, J.-C.: Remarks on the stability of generalized KP solitary waves. In Mathematical problems in the theory of water waves (Luminy, 1995), volume 200 of Contemp. Math., pages 75–84. Amer. Math. Soc., Providence, RI, 1996. [10] de Bouard, A., and Saut, J.-C.: Solitary waves of generalized Kadomtsev-Petviashvili equa- tions. Ann. Inst. Henri Poincar ́e, Analyse Non Lin ́eaire, 14(2):211–236, 1997. [11] de Bouard, A., and Saut, J.-C.: Symmetries and decay of the generalized Kadomtsev- Petviashvili solitary waves. SIAM J. Math. Anal., 28(5):1064–1085, 1997. [12] Ekeland, I.: On the variational principle. J. Math. Anal. Appl., 47:324–353, 1974. [13] Farina, A.: From Ginzburg-Landau to Gross-Pitaevskii. Monatsh. 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Monographs in Harmonic Analysis. Princeton Univ. Press, Princeton, New Jersey, 1993. With the assistance of T.S. Murphy. [40] Tarquini, E ́.: A lower bound on the energy of travelling waves of fixed speed for the Gross- Pitaevskii equation. Monatsh. Math., 151(4):333–339, 2007. [41] Zygmund, A., and Wheeden, Richard L.: Measure and integral : an introduction to real anal- ysis, volume 43 of Monographs and textbooks in pure and applied mathmatics. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4506 | - |
| dc.description.abstract | 本文的目標是探討Fabrice Bethuel,Philippe Gravejat,和 Jean-Claude Saut 在Gross-
Pitaevskii方程式中關於二,三維度的行波解 c∂1u + ∆u + u(1 − |u|2) = 0 前四章節我們透過最小化能量在動量固定下來探討解之存在性,並提供一些構造 這些定理的動機。 最後一章節我們討論Gross-Pitaevskii equation未來的研究方向。 | zh_TW |
| dc.description.abstract | In this thesis, Fabrice Bethuel, Philippe Gravejat, and Jean-Claude Saut discussed the existence of travelling wave solutions to the Gross-Pitaevskii equation in RN , where N = 2, 3.
c∂1u + ∆u + u(1 − |u|2) = 0 In the first four sections, we survey the theorems based on minimizing energy under momentum constraint. Also, we give some motivations about how the theorems are constructed. In the final section, we discuss the future works of Gross-Pitaevskii equation. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:42:48Z (GMT). No. of bitstreams: 1 ntu-104-R01221038-1.pdf: 1051869 bytes, checksum: 0c2d0a9b0f8da8e5d728109f0b5a7158 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 目錄 Contents
致謝 i 中文摘要 ii 英文摘要 iii 1 .Introduction --- 1 2 .Preliminaries --- 12 3. Properties for the function Emin(p) --- 39 4 Proofs for the main results --- 54 5 Future Study on Gross-Pitaevskii equation 70 參考書目 --- 73 | |
| dc.language.iso | en | |
| dc.title | Gross-Pitaevskii方程之行波解 | zh_TW |
| dc.title | Travelling Waves for the Gross-Pitaevskii Equation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林太家,夏俊雄 | |
| dc.subject.keyword | 行波解, | zh_TW |
| dc.subject.keyword | Gross-Pitaevskii,Traveling Waves, | en |
| dc.relation.page | 75 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-08-14 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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| ntu-104-1.pdf | 1.03 MB | Adobe PDF | 檢視/開啟 |
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