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Analysis of a Nonlinear Diffusive Amplitude Equation for Waves on Thin Films
Author(s) -
Melkonian S.,
Maslowe S. A.
Publication year - 1990
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/sapm199082137
Subject(s) - amplitude , nonlinear system , oblique case , mechanics , diffusion , diffusion equation , classical mechanics , physics , tracing , wave equation , mathematical analysis , mathematics , optics , thermodynamics , computer science , philosophy , linguistics , economy , quantum mechanics , economics , service (business) , operating system
This paper presents analytical and numerical solutions of a new amplitude equation governing long waves on thin films. At lowest order in the long‐wave parameter, the equation is nondispersive and represents a balance between nonlinearity and cross‐stream diffusion. Numerical solutions tracing the temporal evolution of an initially localized disturbance indicate that the aforementioned diffusion partly mitigates the tendency of the wave to break. We have also obtained a closed‐form solution resembling an undular bore propagating in an oblique direction.