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The convective viscous Cahn–Hilliard equation: Exact solutions

Published online by Cambridge University Press:  30 June 2015

P. O. MCHEDLOV-PETROSYAN
P. O. MCHEDLOV-PETROSYAN*
Affiliation:
A.I.Akhiezer Institute for Theoretical Physics, National Science Center “Kharkov Institite of Physics & Technology”, 1, Akademicheskaya Str., Kharkov, Ukraine61108 email: peter.mchedlov@free.fr
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Abstract

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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.

Keywords

Cahn–Hilliard equationconvective termviscositytravelling-wave solution
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 42 - 65
Copyright
Copyright © Cambridge University Press 2015 

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