WKB analysis of the Schrödinger-KdV system

Chi Kun Lin, Jun ichi Segata*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number11
Publication statusPublished - 1 Jun 2014
Externally publishedYes


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

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