Dynamics of domain walls governed by the convective Cahn-Hilliard equation

The convective Cahn-Hilliard (CCH) equation, ut+(uxx+u−u3)xx−(D/2)(u2)x=0, has been suggested recently for the description of several physical phenomena, including spinodal decomposition of (driven) phase separating systems in an external field, instability of steps moving on a crystal surface, and faceting of growing, thermodynamically unstable surfaces. In this paper the dynamics of domain walls (kinks) governed by the convective Cahn-Hilliard equation is studied by means of asymptotic and numerical methods. A special attention is paid to the dynamics of kink pairs and triplets that play crucial role in the coarsening (Ostwald ripening) process. For the driving parameter D