Nonlinear self-adjointness, conserved vectors, and traveling wave structures for the kinetics of phase separation dependent on ternary alloys in iron (Fe-Cr-Y (Y = Mo, Cu))

Results in Physics

Naseem Abbas¹  Adil Jhangeer²  Dumitru Baleanu³  Muhammad Bilal Riaz⁴ 

[1] Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Institute of Space Sciences, Magurele, 077125 Bucharest, Romania;Department of Mathematics, Cankaya University, 06530 Ankara, Turkey;Department of Mathematics, University of Management and Technology, Pakistan;

关键词: Convective-diffusive Cahn-Hilliard equation;    Nonlinear self-adjointness;    Direct method;    Similarity reduction;    Solitary wave solutions;   

DOI  :  

来源: DOAJ

【 摘 要 】

The present exploration is concerned with fundamental elements corresponding to the phase decomposition in (Fe-Cr-Mo) and (Fe-Cr-Cu) ternary composites. For the ternary composites of iron, we examine the dynamical behavior of the phase separation. The dynamic of this separation is depicted by a model known as the Cahn-Hilliard equation. The nonlinear self-adjointness for the model under consideration is taken into account. The conserved quantities are calculated with the help of the direct method. For each symmetry generator, we have reduced the considered equation into non-linear ordinary differential equations (ODEs). Also, we have computed the optimal system of the equation under study to find the similarity reduction. Also, the traveling wave structures of the Cahn-Hilliard equation are obtained with the modified simple equation (MSE) technique. Moreover, solitary wave structures is exhibited graphically in the form of 3D, 2D and contour plots.

【 授权许可】

Unknown