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Resonant Triads Involving a Nondispersive Wave
Author(s) -
Rosales Rodolfo R.,
Tabak Esteban G.,
Turner Cristina V.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01426
Subject(s) - quasiperiodic function , homogeneous space , physics , simple (philosophy) , classical mechanics , triad (sociology) , traveling wave , standing wave , breaking wave , mathematical analysis , mathematics , wave propagation , quantum mechanics , geometry , psychology , philosophy , epistemology , psychoanalysis
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.