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Research Article Open access CC BY 4.0

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/v23i430164

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.

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

Cited by 4

A soliton solution of the DD-Equation of the Murnaghan’s rod via the commutative hyper complex analysis

A. Abourabia, Yasser A. Eldreeny · Partial Differential Equations in Applied Mathematics · 2022

Soliton solutions and dynamics of the (3+1)-dimensional Kadomtsev-Petviashvili equation via $ \phi^{6} $-model expansion method

Abid Ullah Khan, Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan, Asif Khan · AIMS Mathematics · 2025

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