Imaging Ultrasound Propagation Using the Westervelt Equation by the Generalized Kudryashov and Modified Kudryashov Methods
Source abstract
Abstract
This article deals with the study of 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. For this reason, the third-order non-linear model of the Westervelt equation was chosen to be studied, as the solutions to such problems have much importance for physical purposes. In this article, we discuss the exact solitary wave solutions of the third-order non-linear model of the Westervelt equation for an acoustic pressure p representing the equation of ultrasound with high intensity, as used in acoustic tomography. Moreover, the non-linear coefficient B/A (being a part of space-dependent coefficient K), has also been investigated in this literature. This problem is solved using the Generalized Kudryashov method along with a comparison of the Modified Kudryashov method. All of the solutions have been discussed with both surface and contour plots, which shows the behavior of the solution. The images are prepared in a well-established way, showing the production of tissues inside the human body.
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Research context
OpenAlex topics: Thermoelastic and Magnetoelastic Phenomena · Geophysics and Sensor Technology · Numerical methods in inverse problems
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics and Statistics, University of Lahore, Lahore 54000, Pakistan
Department of Humanities & Basic Science, Military College of Signals, NUST, Islamabad 44000, Pakistan
Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138 Nicosia, Turkey
Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain
Funding
Basque Government · MCIN/AEI 269.10.13039/501100011033
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