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Direct Resonance in Double‐Diffusive Systems
Author(s) -
Maslowe S. A.
Publication year - 1985
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 - 10.1002/sapm198573159
Subject(s) - amplitude , instability , nonlinear system , resonance (particle physics) , generalization , parameter space , point (geometry) , physics , convection , space (punctuation) , stability (learning theory) , mathematical analysis , classical mechanics , mathematics , statistical physics , mechanics , optics , computer science , quantum mechanics , geometry , operating system , machine learning
In thermohaline convection and a number of other systems, both direct and oscillatory modes of instability are possible. Should these modes coalesce at some point in parameter space, nonlinear instabilities are likely to be more dramatic in the neighborhood of such a point than elsewhere. A finite‐amplitude evolution equation describing such events is derived here by the method of multiple scales. The results are compared with those obtained previously for model systems and by other methods. The direct resonance point of view is found to provide some new insights. A generalization to allow for slow spatial modulation of the amplitude is given and, among other possibilities, solitary‐wave solutions are obtainable.