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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 <i>p</i> representing the equation of ultrasound with high intensity, as used in acoustic tomography. Moreover, the non-linear coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mo>/</mo><mi>A</mi></mrow></semantics></math></inline-formula> (being a part of space-dependent coefficient <i>K</i>), 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.