Reaction-diffusion systems and nonlinear waves

Abstract

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.

LaTeX, 16 pages, corrected typos

References in corpus (5)

• On Generalized Fractional Kinetic Equations
• On Fractional Kinetic Equations
• Fractional reaction-diffusion equations
• Unified Fractional Kinetic Equation and a Fractional Diffusion Equation
• Astrophysical Thermonuclear Functions for Boltzmann-Gibbs Statistics and Tsallis Statistics

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