The convective viscous Cahn–Hilliard equation: Exact solutions

Author:

MCHEDLOV-PETROSYAN P. O.

Abstract

In this paper, we give exact solutions for the convective viscous Cahn--Hilliard equation. This equation with a general symmetric double-well potential and Burgers-type convective term was introduced by T. P. Witelski (1996 Studies in Applied Mathematics96, 277–300) to study the joint effects of nonlinear convection and viscosity. We consider this equation with a polynomial, generally asymmetric potential. We also consider both Burgers-type and cubic convective terms. We obtained exact travelling-wave solutions for both cases. For the former case, with an additional constraint on nonlinearity and viscosity, we also obtained an exact two-wave solution.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics

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