抄録
We consider the behavior of solutions to the water wave interaction equations in the limit ε→0+. To justify the semiclassical approximation, we reduce the water wave interaction equation into some hyperbolic-dispersive system by using a modified Madelung transform. The reduced system causes loss of derivatives which prevents us to apply the classical energy method to prove the existence of solution. To overcome this difficulty we introduce a modified energy method and construct the solution to the reduced system.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 3817-3834 |
| ページ数 | 18 |
| ジャーナル | Journal of Differential Equations |
| 巻 | 256 |
| 発行部数 | 11 |
| DOI | |
| 出版物ステータス | 出版済み - 6 1 2014 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
これを引用
WKB analysis of the Schrödinger-KdV system. / Lin, Chi Kun; Segata, Junichi.
：: Journal of Differential Equations, 巻 256, 番号 11, 01.06.2014, p. 3817-3834.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - WKB analysis of the Schrödinger-KdV system
AU - Lin, Chi Kun
AU - Segata, Junichi
PY - 2014/6/1
Y1 - 2014/6/1
N2 - We consider the behavior of solutions to the water wave interaction equations in the limit ε→0+. To justify the semiclassical approximation, we reduce the water wave interaction equation into some hyperbolic-dispersive system by using a modified Madelung transform. The reduced system causes loss of derivatives which prevents us to apply the classical energy method to prove the existence of solution. To overcome this difficulty we introduce a modified energy method and construct the solution to the reduced system.
AB - We consider the behavior of solutions to the water wave interaction equations in the limit ε→0+. To justify the semiclassical approximation, we reduce the water wave interaction equation into some hyperbolic-dispersive system by using a modified Madelung transform. The reduced system causes loss of derivatives which prevents us to apply the classical energy method to prove the existence of solution. To overcome this difficulty we introduce a modified energy method and construct the solution to the reduced system.
UR - http://www.scopus.com/inward/record.url?scp=84897391446&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84897391446&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2014.03.001
DO - 10.1016/j.jde.2014.03.001
M3 - Article
AN - SCOPUS:84897391446
VL - 256
SP - 3817
EP - 3834
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 11
ER -