Traveling wave speed and solution in reaction-diffusion equation in one dimension

By Painleve analysis, traveling wave speed and solution of reaction-diffusi on equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is large r than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, th e other with the series expansion solution, also yielding the value of spee d. Conversely, when the exponent of creation term is smaller than the one o f the annihilation term, two typical cases are also studied, but only for o ne of them, there is a series development solution, yielding the value of s peed, and for the other, traveling wave solution cannot exist. Besides, the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.