Analytical Solution of the Complex Polymer Equation Systems via the Homogeneous Balance Method

Aly M. Abourabia *

Department of Mathematics, Faculty of Science, Menoufiya University, Shebin Elkom 32511, Egypt.

Yasser A. Eldreeny

Department of Mathematics, Faculty of Science, Menoufiya University, Shebin Elkom 32511, Egypt.

*Author to whom correspondence should be addressed.


Abstract

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.

Keywords: Polymers, laser ablation, Doubly Dispersive Equation (DDE), travelling wave variable, normal dispersion, strain, homogeneous balance method, soliton solutions


How to Cite

Abourabia, A. M., & Eldreeny, Y. A. (2019). Analytical Solution of the Complex Polymer Equation Systems via the Homogeneous Balance Method. Physical Science International Journal, 23(4), 1–8. https://doi.org/10.9734/psij/2019/v23i430164

Downloads

Download data is not yet available.