WKB analysis of the Schrödinger-KdV system

Chi Kun Lin, Jun ichi Segata

Research output: Contribution to journalArticlepeer-review

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 - 2014 Jun 1

Keywords

  • System of dispersive equations
  • WKB analysis
  • Well-posedness
  • Zero dispersion limit

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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