In this talk, nonlinear advection-diffusion equations, previously designed for image denoising and edge detection, are introduced. Each of the equations combines Burgers’s convection with a nonlinear diffusion, and one of the equations was proposed by Perona and Malik. We study the existence of traveling wave solutions of the equations. Particularly for Perona and Malik’s equation, we investigate the nonlinear stability of traveling waves by considering more general diffusion and convection terms.