Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis

Zehra Pinar Izgi, Pshtiwan Othman Mohammed (), Ravi P. Agarwal, Majeed A. Yousif, Alina Alb Lupas () and Mohamed Abdelwahed
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Zehra Pinar Izgi: Department of Mathematics, Faculty of Arts and Science, Tekirdağ Namık Kemal University, 59030 Tekirdağ, Turkey
Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
Ravi P. Agarwal: Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Majeed A. Yousif: Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq
Alina Alb Lupas: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Mohamed Abdelwahed: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-9

Abstract: Metamaterials have emerged as a focal point in contemporary science and technology due to their ability to drive significant innovations. These engineered materials are specifically designed to couple the phenomena of different physical natures, thereby influencing processes through mechanical or thermal effects. While much of the recent research has concentrated on frequency conversion into electromagnetic waves, the field of acoustic frequency conversion still faces considerable technical challenges. To overcome these hurdles, researchers are developing metamaterials with customized acoustic properties. A key equation for modeling nonlinear acoustic wave phenomena is the dissipative Westervelt equation. This study investigates analytical solutions using ansatz-based methods combined with Lie symmetries. The approach presented here provides a versatile framework that is applicable to a wide range of fields in metamaterial design.

Keywords: Westervelt equation; metamaterials; ansatz-based methods; symmetry analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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