On the μ-transform: Applications to the Cahn-Hilliard equation

The μ-transform was recently introduced and applied to finding exact solutions of some well known nonlinear evolutionary models. In this Letter two new applications of this transform to the Cahn-Hilliard equation are presented. Firstly, an exact solution of this equation with the cubic potential, u‵=(au2+bu−u″)″, is derived. This solution scales with the Lifshitz-Slezov exponent of 1/3. Secondly, an exact solution of a nonlinear parabolic equation u′=(∂F/∂u)″ with a potential F=ulnu+(1−u)ln(1−u) describing the equilibration of a binary mixture in the process of annealing is derived. The procedure of applying the μ-transform is thoroughly discussed.