Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

摘要

The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations u(t) = u(xx) + alpha[beta H(u-theta)-u] w, wt = s(u yw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation u(t) = u(xx) + alpha[beta H (u-theta)-u], under different conditions on the model constants.