General set of traveling-wave solutions for amplitude equations in the phase field crystal model

International Conference "Structural and Phase Transformations in Materials: Theory, Computer Modelling and Experiment"

材料科学;计算机科学

Nizovtseva, I.G.^1,2 ; Galenko, P.K.^1,2

Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät, Jena

D-07743, Germany^1

Ural Federal University, Department of Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ekaterinburg

620000, Russia^2

关键词: Allen-Cahn equation;    Amplitude equation;    Atomic density;    Crystalline state;    Homogeneous state;    Hyperbolic equations;    Phase field crystal model;    Traveling wave solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/192/1/012004/pdf
DOI  :  10.1088/1757-899X/192/1/012004

来源: IOP

【 摘 要 】

Fronts dynamics of periodic crystalline state, which invades the homogeneous state (liquid phase), are analysed. These fronts are considered as traveling waves of atomic density amplitudes. The propagation of amplitudes is described by the hyperbolic equation of an extended Allen-Cahn type for which the complete set of analytical traveling-wave solutions are obtained by tanh-method. The set of solutions includes previously known traveling waves for the parabolic Allen-Cahn equation of both extended and standard form.