Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes

In this paper, different traveling wave solutions of the kink type are obtained for significant advection-diffusion-reaction mechanisms such as the singularly perturbed generalized Burgers Huxley and Burgers Fisher equations. To achieve this, a nonlinear transformation and an ansatz method have been utilized. Stability analysis is performed on different types of equations to detect the effects of the coefficients on the stability of the obtained solutions. Particularly under advection dominant cases, the stability of the derived solutions is examined separately. It is observed that especially the coefficient of nonlinearity, and partly one of the reaction coefficients, determine the stability behaviour under advection dominance.