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Study of phase separation process in multi-component mixtures using analytical methods and decomposition variational
Jiaming Luo1, Jalil Manafian2,3, Arezu Aghazadeh4,5
1School of Mathematics and Statistics, Kashi University, No. 380, Xuefu Avenue, Kashi, Xinjiang, 844000, China.
Scientific Reports
|November 5, 2025
Summary
This study explores the fourth-order Cahn-Hilliard equation, crucial for understanding phase separation dynamics. Researchers used multiple methods to find exact traveling wave solutions, revealing diverse soliton types for complex physical phenomena.
Area of Science:
- Applied Physics and Engineering
- Nonlinear Dynamics
- Materials Science
Background:
- The fourth-order Cahn-Hilliard equation models critical phenomena like spinodal decomposition and phase separation.
- Understanding these dynamics is vital for materials science and fluid mechanics.
Purpose of the Study:
- To investigate exact traveling wave solutions for the fourth-order Cahn-Hilliard equation.
- To explore the application of various analytical methods in solving nonlinear evolution equations (NLEEs).
Main Methods:
- The study employed the [Formula: see text]-expansion method (TEM).
- Jacobi elliptic function expansion scheme (JEFES) was utilized.
- Rational multi wave functions (RMWFs) and decomposition variational iteration method (DVIM) were also applied.
Main Results:
- Distinct traveling wave solutions were identified, including dark, bright, kink, singular, and combined soliton types.
- The dynamics of these solutions were visualized using 3D, 2D, contour, and density plots.
- The decomposition variational iteration method was analyzed, with conditions developed.
Conclusions:
- The applied methods successfully identified various soliton solutions, demonstrating their efficacy for NLEEs.
- These findings offer insights into complex physical phenomena and potential applications in areas like optical memories.
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