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New soliton solutions of M-fractional Westervelt model in ultrasound imaging via two analytical techniques

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Abstract

This research paper is about the ultrasound propagation, which propagates the mechanical vibration of the molecules or of the particles of a material. It measures the speed of sound in air. Ultrasound imaging is being used in a well-established way to produce pictures of tissues inside the body of human beings. They are modeled in non-linear wave equations with high intensity. We obtained the new soliton solutions to the M-fractional (\(1+1\))-dimensional nonlinear Westervelt model by utilizing \(\exp _a\) function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. The stability of the concerned model is also discussed. The images are prepared in a well-established way, showing the production of tissues inside the human body. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman, 11733, Jordan

    Haitham Qawaqneh

  2. Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, Pakistan

    Asim Zafar & Muhammad Raheel

  3. Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan, 45142, Saudi Arabia

    Abdullah A. Zaagan

  4. Department of Basic Science, Faculty of Engineering, Benha University, Shubra, Egypt

    Emad H. M. Zahran

  5. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

    Adem Cevikel

  6. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

Authors
  1. Haitham Qawaqneh
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  2. Asim Zafar
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  3. Muhammad Raheel
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  4. Abdullah A. Zaagan
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  5. Emad H. M. Zahran
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  6. Adem Cevikel
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  7. Ahmet Bekir
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Contributions

Haitham Qawaqneh: Conceptualization, project administration. Asim Zafar: Formal analysis and investigation, writing original draft. M. Raheel: Software, visualization. Abdullah A. Zaagan: Scientific computing, review and editing. Emad H.M. Zahran: Formal analysis and investigation, methodology. Adem Cevikel: Validation, review and editing. Ahmet Bekir: Supervision, Conceptualization, methodology.

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Correspondence to Ahmet Bekir.

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Qawaqneh, H., Zafar, A., Raheel, M. et al. New soliton solutions of M-fractional Westervelt model in ultrasound imaging via two analytical techniques. Opt Quant Electron 56, 737 (2024). https://doi.org/10.1007/s11082-024-06371-1

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