Sixth order modification of the Cahn-Hilliard equation

TL;DR

This paper introduces a sixth-order variant of the Cahn-Hilliard equation with a parameter-dependent gradient coefficient and additional nonlinear terms, providing exact solutions and analyzing their parameter dependence.

Contribution

It presents a novel sixth-order modification of the Cahn-Hilliard equation with exact solutions and explores the influence of parameters on these solutions.

Findings

Derived exact static and traveling wave solutions.

Analyzed how system parameters affect solution behavior.

Extended understanding of higher-order phase separation models.

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.