Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

New Soliton Solutions of M-fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques

Version 1 : Received: 29 September 2023 / Approved: 30 September 2023 / Online: 30 September 2023 (08:53:07 CEST)

A peer-reviewed article of this Preprint also exists.

Qawaqneh, H.; Zafar, A.; Raheel, M.; Zaagan, A.A.; Zahran, E.H.M.; Cevikel, A.; Bekir, A. New Soliton Solutions of M-Fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques. Optical and Quantum Electronics 2024, 56, doi:10.1007/s11082-024-06371-1. Qawaqneh, H.; Zafar, A.; Raheel, M.; Zaagan, A.A.; Zahran, E.H.M.; Cevikel, A.; Bekir, A. New Soliton Solutions of M-Fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques. Optical and Quantum Electronics 2024, 56, doi:10.1007/s11082-024-06371-1.

Abstract

This research paper is about to obtain 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. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

Keywords

M-fractional Westervelt model; The $\exp_a$ function technique; Modified simplest equation technique; Exact solutions

Subject

Computer Science and Mathematics, Applied Mathematics

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