High frequency perturbation of cnoidal waves in KdV

Research output: Contribution to journalArticlepeer-review


The KdV equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy (L2 norm) is studied. It is proved that the interaction of a low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately satisfies the Airy equation.

Original languageEnglish (US)
Pages (from-to)4147-4164
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - 2012


  • High frequency
  • KdV cnoidal waves
  • Korteweg-de Vries

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'High frequency perturbation of cnoidal waves in KdV'. Together they form a unique fingerprint.

Cite this