New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod
By Aly R. Seadawy, Jalil Manafian. 2018
146 citations recorded by the source corpus.
Abstract This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.
Subfields: Mechanics of Materials, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3b9433234bbb75d673e5a59979239f4df044109d
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In Mechanics of Materials
In Statistical and Nonlinear Physics
Citations in the corpus
- Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity (2019, background): “(a) Dark soliton solution for Equation (23) and (b) Kink wave soliton solution for Equation (24).”