Exact Solution for Nonlinear Acoustics Model with Conformable Derivative
In this study, we investigate the analytical solutions of the Zabolotskaya–Khokhlov (ZK) equation, which describes the propagation of nonlinear acoustic waves with diffraction effects in a medium. Its physical significance lies in modeling the behavior of high-amplitude sound waves, where nonlinear...
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Mahmut Akyigit
2025-03-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4294446 |
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| author | Orkun Taşbozan Ali Kurt |
| author_facet | Orkun Taşbozan Ali Kurt |
| author_sort | Orkun Taşbozan |
| collection | DOAJ |
| description | In this study, we investigate the analytical solutions of the Zabolotskaya–Khokhlov (ZK) equation, which describes the propagation of nonlinear acoustic waves with diffraction effects in a medium. Its physical significance lies in modeling the behavior of high-amplitude sound waves, where nonlinear effects (such as wave steepening) and diffraction (spreading of the wave in directions perpendicular to the main propagation axis) both play an important role. In the ZK equation, time derivatives are described in terms of conformable derivatives, which have gained popularity recently and have drawn attention from numerous studies. It offers nearly all the fundamental characteristics of the classical derivative in the Newtonian style, and it looks into the precise solution of the mathematical model this derivative expresses. Also sub-equation method is used as a tool for obtaining the analytical results. 3D graphical illustrations are given to express the physical behavior of obtained results. |
| format | Article |
| id | doaj-art-268e14b120ca446eb0f2d0a001d6f010 |
| institution | OA Journals |
| issn | 2636-8692 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj-art-268e14b120ca446eb0f2d0a001d6f0102025-08-20T02:19:44ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922025-03-0181222710.33187/jmsm.15688361408Exact Solution for Nonlinear Acoustics Model with Conformable DerivativeOrkun Taşbozan0https://orcid.org/0000-0001-5003-6341Ali Kurt1https://orcid.org/0000-0002-0617-6037HATAY MUSTAFA KEMAL UNIVERSITYPAMUKKALE UNIVERSITYIn this study, we investigate the analytical solutions of the Zabolotskaya–Khokhlov (ZK) equation, which describes the propagation of nonlinear acoustic waves with diffraction effects in a medium. Its physical significance lies in modeling the behavior of high-amplitude sound waves, where nonlinear effects (such as wave steepening) and diffraction (spreading of the wave in directions perpendicular to the main propagation axis) both play an important role. In the ZK equation, time derivatives are described in terms of conformable derivatives, which have gained popularity recently and have drawn attention from numerous studies. It offers nearly all the fundamental characteristics of the classical derivative in the Newtonian style, and it looks into the precise solution of the mathematical model this derivative expresses. Also sub-equation method is used as a tool for obtaining the analytical results. 3D graphical illustrations are given to express the physical behavior of obtained results.https://dergipark.org.tr/en/download/article-file/4294446analytical solutionconformable fractional derivativefractional calculusnonlinear acoustics |
| spellingShingle | Orkun Taşbozan Ali Kurt Exact Solution for Nonlinear Acoustics Model with Conformable Derivative Journal of Mathematical Sciences and Modelling analytical solution conformable fractional derivative fractional calculus nonlinear acoustics |
| title | Exact Solution for Nonlinear Acoustics Model with Conformable Derivative |
| title_full | Exact Solution for Nonlinear Acoustics Model with Conformable Derivative |
| title_fullStr | Exact Solution for Nonlinear Acoustics Model with Conformable Derivative |
| title_full_unstemmed | Exact Solution for Nonlinear Acoustics Model with Conformable Derivative |
| title_short | Exact Solution for Nonlinear Acoustics Model with Conformable Derivative |
| title_sort | exact solution for nonlinear acoustics model with conformable derivative |
| topic | analytical solution conformable fractional derivative fractional calculus nonlinear acoustics |
| url | https://dergipark.org.tr/en/download/article-file/4294446 |
| work_keys_str_mv | AT orkuntasbozan exactsolutionfornonlinearacousticsmodelwithconformablederivative AT alikurt exactsolutionfornonlinearacousticsmodelwithconformablederivative |