On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system
Abstract This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many...
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Nature Portfolio
2024-10-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-75494-y |
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| author | Usman Younas Jan Muhammad Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Z. Jan |
| author_facet | Usman Younas Jan Muhammad Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Z. Jan |
| author_sort | Usman Younas |
| collection | DOAJ |
| description | Abstract This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many different uses in the area include transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, techniques for measuring blood flow and tissue motion, and three-dimensional imaging. The third-order non-linear $$\beta$$ β -fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The exact solutions of different types, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted. These solutions are obtained by using two newly introduced techniques, namely modified generalized Riccati equation mapping method and modified generalized exponential rational function method. Moreover, breather, lump and other waves are extracted by the assistance of logarithmic transformation and different test functions. The used methodologies are extremely effective and possess substantial computing capacity to effectively address the different solutions with a high level of accuracy in these systems. The techniques used are well-known for being effective, simple, and flexible enough to integrate multiple soliton systems into a unified framework. In addition, we provide 2D and 3D graphs that explain the behavior of the solution at various parameter values, under the influence of $$\beta$$ β -fractional derivatives. The results offered in this study may improve the comprehension of the nonlinear dynamic behavior of the specific system and confirm the efficacy of the approaches used. We expect that our approaches will be beneficial for a wide range of nonlinear models and other problems in the related fields. |
| format | Article |
| id | doaj-art-3312bb727674489eb4bb332b93eddfc4 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-3312bb727674489eb4bb332b93eddfc42025-08-20T02:18:31ZengNature PortfolioScientific Reports2045-23222024-10-0114111510.1038/s41598-024-75494-yOn the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear systemUsman Younas0Jan Muhammad1Qasim Ali2Mirwais Sediqmal3Krzysztof Kedzia4Ahmed Z. Jan5Department of Mathematics, Shanghai UniversityDepartment of Mathematics, Shanghai UniversityDepartment of Mathematics, University of the ChakwalFaculty of Civil Engineering Laghman UniversityDepartament of Mechanical Engineering, Wrocław University of Science and TechnologyDepartament of Mechanical Engineering, Wrocław University of Science and TechnologyAbstract This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many different uses in the area include transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, techniques for measuring blood flow and tissue motion, and three-dimensional imaging. The third-order non-linear $$\beta$$ β -fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The exact solutions of different types, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted. These solutions are obtained by using two newly introduced techniques, namely modified generalized Riccati equation mapping method and modified generalized exponential rational function method. Moreover, breather, lump and other waves are extracted by the assistance of logarithmic transformation and different test functions. The used methodologies are extremely effective and possess substantial computing capacity to effectively address the different solutions with a high level of accuracy in these systems. The techniques used are well-known for being effective, simple, and flexible enough to integrate multiple soliton systems into a unified framework. In addition, we provide 2D and 3D graphs that explain the behavior of the solution at various parameter values, under the influence of $$\beta$$ β -fractional derivatives. The results offered in this study may improve the comprehension of the nonlinear dynamic behavior of the specific system and confirm the efficacy of the approaches used. We expect that our approaches will be beneficial for a wide range of nonlinear models and other problems in the related fields.https://doi.org/10.1038/s41598-024-75494-yModified generalized Riccati equation mapping and generalized exponential rational function methodsInteraction solutionsSolitonsWestervelt equationUltrasound imaging$$\beta$$ β -fractional derivatives |
| spellingShingle | Usman Younas Jan Muhammad Qasim Ali Mirwais Sediqmal Krzysztof Kedzia Ahmed Z. Jan On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system Scientific Reports Modified generalized Riccati equation mapping and generalized exponential rational function methods Interaction solutions Solitons Westervelt equation Ultrasound imaging $$\beta$$ β -fractional derivatives |
| title | On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| title_full | On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| title_fullStr | On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| title_full_unstemmed | On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| title_short | On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| title_sort | on the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system |
| topic | Modified generalized Riccati equation mapping and generalized exponential rational function methods Interaction solutions Solitons Westervelt equation Ultrasound imaging $$\beta$$ β -fractional derivatives |
| url | https://doi.org/10.1038/s41598-024-75494-y |
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