用分析方法和分解变量代方法研究多元组分混合物的相位分离过程,用于第四阶级的卡恩-希利亚德方程
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
概括
本研究探讨了第四阶级的Cahn-Hilliard方程,对于理解相位分离动态至关重要. 研究人员使用多种方法找到精确的移动波解决方案,揭示了复杂物理现象的多种单体类型.
科学领域:
- 应用物理与工程应用物理与工程
- 非线性动力学是一种非线性动力学.
- 材料科学 材料科学 材料科学
背景情况:
- 第四阶卡恩-希利亚德方程模拟了诸如旋点分解和相分离之类的关键现象.
- 了解这些动态对于材料科学和流体力学至关重要.
研究的目的:
- 为了研究第四阶卡恩-希利亚德方程的确切旅行波解决方案.
- 探索各种分析方法在解决非线性进化方程 (NLEE) 的应用.
主要方法:
- 这项研究采用了[公式:参见文本]扩展方法 (TEM).
- 使用了雅科比圆函数扩展方案 (JEFES).
- 理性多波函数 (RMWF) 和分解变量代方法 (DVIM) 也被应用.
主要成果:
- 确定了不同的移动波解决方案,包括黑暗,明亮,扭曲,单一和组合单一类型.
- 这些解决方案的动态可视化使用3D,2D,轮和密度图.
- 分析了分解变量代方法,并开发了条件.
结论:
- 应用的方法成功地确定了各种单离子溶液,证明了它们对NLEE的有效性.
- 这些发现提供了对复杂物理现象的洞察力,以及在光学记忆等领域的潜在应用.
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