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The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior

Author

Listed:
  • Zhi-Yong Zhang

    (College of Science, Minzu University of China, Beijing 100081, P. R. China)

  • Kai-Hua Ma

    (#x2020;College of Science, North China University of Technology, Beijing 100144, P. R. China)

  • Li-Sheng Zhang

    (#x2020;College of Science, North China University of Technology, Beijing 100144, P. R. China)

Abstract

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

Suggested Citation

  • Zhi-Yong Zhang & Kai-Hua Ma & Li-Sheng Zhang, 2020. "The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-17, February.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:02:n:s0129183120500242
    DOI: 10.1142/S0129183120500242
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