发表机构
National Science Center Kharkiv Institute of Physics and Technology; Ukrainian State University of Railway Transport（哈尔科夫物理与技术国家科学中心; 乌克兰国立铁路运输大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨Cahn-Hilliard方程中迁移率对序参量的依赖，提出倒数线性和二次依赖关系，并求得精确行波解，发现倒数二次迁移率在有限参数区间内可良好近似多项式迁移率。
AI 中文摘要
一般来说，Cahn-Hilliard方程中的迁移率可能依赖于序参量；这一点在最初的推导中就已经很明显。然而，显式引入这种依赖关系会导致巨大的计算困难，因此常数迁移率近似被普遍使用。另一方面，在某些情况下，这种依赖关系显得至关重要，因此应用了更现实的表达式，通常是正幂或多项式；尽管如此，对于这样的依赖关系，只存在近似解和/或数值解。我们考虑了迁移率对序参量的‘倒数’线性和二次依赖关系；对于这些依赖关系，获得了精确的行波解。更有甚者，在参数的一个有限区间内，倒数二次迁移率是多项式迁移率的相当好的近似。
英文摘要
Generally the mobility in the Cahn-Hilliard equation may depend on the order parameter; this was evident already from the original derivation. However, explicit introduction of such dependence results in tremendous calculation difficulties, so the constant mobility approximation was commonly used. On the other hand, in several cases this dependence appeared to be crucial, so more realistic expressions were applied, usually positive powers or polynomials; still, for such dependencies only approximate and/or numerical solution exist. We consider 'reciprocal' linear and quadratic dependencies of mobility on the order parameter; for these dependencies exact traveling wave solutions are obtained. Even more, in a limited interval of the parameters reciprocal quadratic mobilities are rather good approximations to polynomial mobilities.
Comments16 pages, 2 figures, two-column format
