Resonant triads involving a nondispersive wave

Rodolfo R. Rosales, Esteban G. Tabak, Cristina V. Turner

Research output: Contribution to journalArticle

Abstract

A simple system is studied, involving a single nondispersive breaking wave and its interaction with two dispersive modes through a resonant triad. The dynamics of this system are shown to be quite rich, through a combined theoretical and numerical analysis. A sharply defined traveling wave with a corner seems to attract almost all initial data with enough energy, provided the nondispersive wave is unstable to the other two when standing alone. In other cases, the solution converges to quasiperiodic final states, unless extra symmetries force the solution to converge to simpler configurations.

Original languageEnglish (US)
Pages (from-to)105-122
Number of pages18
JournalStudies in Applied Mathematics
Volume108
Issue number1
DOIs
StatePublished - Jan 2002

ASJC Scopus subject areas

  • Applied Mathematics

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