Series solution of nonlinear coupled reaction-diffusion equations

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Abstract
A nonlinear set of two coupled reaction-diffusion equations is investigated analytically to obtain travelling wave solutions. First, the series method of Hereman et al (1990), involving powers of decaying exponentials, is used to determine the width and the velocity of those waves. Further, to get a suitable analytical expression for them, another power series is introduced for which now a tanh function acts as a new variable. As a result, recursion relations can be set up. Keeping only the lowest order terms, neglecting coefficients of higher order, the author finds solutions which correspond with earlier numerical calculations.