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Asymptotic Solutions of the Field‐Noyes Model for the Belousov Reaction—II. Plane Waves
Author(s) -
Stanshine J. A.
Publication year - 1976
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/sapm1976554327
Subject(s) - wavelength , homogeneous , plane wave , reaction–diffusion system , plane (geometry) , perturbation (astronomy) , long wavelength limit , parametric statistics , physics , field (mathematics) , classical mechanics , mathematical analysis , mathematics , optics , statistical physics , geometry , thermodynamics , quantum mechanics , statistics , pure mathematics
The spatially homogeneous limit cycle solutions found by Stanshine and Howard [7] for the Field‐Noyes model of the Belousov reaction are used to obtain plane wave solutions for the related reaction‐diffusion equations. Perturbation techniques are implemented first to find long wavelength waves and then successively to find shorter wavelength waves. Plane wave solutions are then shown to exist for sufficiently short wavelengths for parametric values which are physically plausible but for which spatially homogeneous oscillations do not (apparently) exist.