Zero-dispersion limit of the short-wave-long-wave interaction equations

Chi Kun Lin*, Yau Shu Wong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


The purpose of this paper is to study the zero-dispersion limit of the water wave interaction equations which arise in modelling surface waves in the present of both gravity and capillary modes. This topic is also of interest in plasma physics. For the smooth solution, the limiting equation is given by the compressible Euler equation with a nonlocal pressure caused by the long wave. For weak solution, when the coupling coefficient λ is small order of ε, λ = o (ε), the wave map equation is derived and the scattering sound wave is shown to satisfy a linear wave equation.

Original languageEnglish
Pages (from-to)87-110
Number of pages24
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 1 Sept 2006
Externally publishedYes


  • Dispersive perturbation
  • Long wave
  • Quasilinear hyperbolic system
  • Scattering sound wave
  • Semiclassical limit
  • Short wave
  • WKB analysis
  • Zero-dispersion limit

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