Sixth order modification of the Cahn-Hilliard equation
Statistical Mechanics
2026-02-09 v1
Abstract
We consider the sixth-order convective-viscous Cahn-Hilliard equation, different from the standard fourth-order Cahn-Hilliard equation due to the modified expression for the thermodynamic potential. In such modified thermodynamic potential the coefficient at the square gradient term is order-parameter-dependent. It also contains the square of the Laplacian. This results in a sixth-order differential equation and additional nonlinear terms in the equation. We obtained several exact static- and traveling wave solutions and studied the dependence of solutions on the parameters of the system.
Cite
@article{arxiv.2602.06571,
title = {Sixth order modification of the Cahn-Hilliard equation},
author = {P. O. Mchedlov-Petrosyan and L. N. Davydov and O. A. Osmaev},
journal= {arXiv preprint arXiv:2602.06571},
year = {2026}
}
Comments
arXiv admin note: text overlap with arXiv:2412.03156