WKB analysis of the Schrödinger-KdV system

Chi Kun Lin, Junichi Segata

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)3817-3834
Number of pages18
JournalJournal of Differential Equations
Volume256
Issue number11
DOIs
Publication statusPublished - Jun 1 2014
Externally publishedYes

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Water waves
Korteweg-de Vries Equation
Wave Interaction
Water Waves
Energy Method
Semiclassical Approximation
Behavior of Solutions
Derivatives
Justify
Existence of Solutions
Transform
Derivative

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

WKB analysis of the Schrödinger-KdV system. / Lin, Chi Kun; Segata, Junichi.

In: Journal of Differential Equations, Vol. 256, No. 11, 01.06.2014, p. 3817-3834.

Research output: Contribution to journalArticle

Lin, Chi Kun ; Segata, Junichi. / WKB analysis of the Schrödinger-KdV system. In: Journal of Differential Equations. 2014 ; Vol. 256, No. 11. pp. 3817-3834.
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