On the Modified Eguchi-Oki-Matsumura System

TL;DR

This paper investigates a modified version of the Eguchi-Oki-Matsumura system, revealing that with a convective-viscous Cahn-Hilliard dynamic, the system admits exact traveling wave solutions, advancing understanding of phase transition models.

Contribution

It introduces a modification to the Eguchi-Oki-Matsumura system and demonstrates the existence of exact traveling wave solutions under specific dynamics.

Findings

Exact traveling wave solutions found for the modified system.

The model extends the understanding of phase transition dynamics.

The system's behavior aligns with type C models in Hohenberg-Halperin classification.

Abstract

To describe the simultaneous order-disorder transformation and phase separation Eguchi, Oki and Matsumura [\doi{10.1557/proc-21-589}] introduced the system of two equations: one equation, governing the evolution of a conserved order parameter, and the second equation for the non-conserved order parameter. The key feature of their model is the free energy functional, which contains the square gradient terms of the both order parameters and a fourth power polynomial depending on both order parameters. According to the general Hohenberg-Halperin classification it is the type C model. We show that if the dynamics of the conserved order parameter is governed by the convective-viscous Cahn-Hilliard equation, this system allows exact traveling wave solution.