Analytical Solution of the Complex Polymer Equation Systems via the Homogeneous Balance Method
Aly M. Abourabia, Yasser A. Eldreeny
Physical Science International Journal · pp. 1–8 · Published 19 Dec 2019
10.9734/psij/2019/v23i430164Abstract
In this article, we solve analytically the nonlinear Doubly Dispersive Equation (DDE) in (1+1)-D by the homogeneous balance method, introduced to investigate the strain waves propagating in a cylindrical rod in complex polymer systems. The linear dispersion relation plays important role in connecting the frequency of the emitted nonlinear waves with the wave number of the ablating laser beam affecting the polymers with their characteristic parameters. In accordance with the normal dispersion conditions, the resulting solitary wave solutions show the compression characters in the nonlinearly elastic materials namely Polystyrene (PS) and PolyMethylMethAcrylate (PMMA). The ratio between the estimated potential and kinetic energies shows good agreement with the physical situation, and as well in making comparisons with the bell-shaped model conducted in the literature.
Cited by 4
M. Qasim, F. Yao, H. Ismael · The European Physical Journal Plus · 2025
A. Abourabia, Yasser A. Eldreeny · Partial Differential Equations in Applied Mathematics · 2022
Xiao-Feng Yang, Yi Wei · 2020
Abid Ullah Khan, Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan, Asif Khan · AIMS Mathematics · 2025
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