WKB analysis of the Schrödinger-KdV system

Chi Kun Lin; Jun ichi Segata

doi:10.1016/j.jde.2014.03.001

WKB analysis of the Schrödinger-KdV system

Chi Kun Lin, Jun ichi Segata

研究成果: Contribution to journal › Article › 査読

1 被引用数 (Scopus)

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.

本文言語	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
号	11
DOI	https://doi.org/10.1016/j.jde.2014.03.001
出版ステータス	出版済み - 6 1 2014
外部発表	はい

All Science Journal Classification (ASJC) codes

分析
応用数学

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10.1016/j.jde.2014.03.001

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引用スタイル

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title = "WKB analysis of the Schr{\"o}dinger-KdV system",

abstract = "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.",

author = "Lin, {Chi Kun} and Segata, {Jun ichi}",

note = "Funding Information: J.S. is partially supported by MEXT , Grant-in-Aid for Young Scientists (B) 21740122 . Part of this work was done when he visited CMMSC of NCTU in Taiwan, he would like to thank their support and hospitality during his visit. C.K. Lin is partially supported by National Science Council of Taiwan under the grant NSC101-2115-M-009-008-MY2 .",

year = "2014",

month = jun,

day = "1",

doi = "10.1016/j.jde.2014.03.001",

language = "English",

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journal = "Journal of Differential Equations",

issn = "0022-0396",

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T1 - WKB analysis of the Schrödinger-KdV system

AU - Lin, Chi Kun

AU - Segata, Jun ichi

N1 - Funding Information: J.S. is partially supported by MEXT , Grant-in-Aid for Young Scientists (B) 21740122 . Part of this work was done when he visited CMMSC of NCTU in Taiwan, he would like to thank their support and hospitality during his visit. C.K. Lin is partially supported by National Science Council of Taiwan under the grant NSC101-2115-M-009-008-MY2 .

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.

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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 -

WKB analysis of the Schrödinger-KdV system

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