Exact Solution for Nonlinear Acoustics Model with Conformable Derivative

Year 2025, , 22 - 27, 28.03.2025

Ali Kurt , Orkun Taşbozan

https://doi.org/10.33187/jmsm.1568836

Abstract

In this study, we investigate the analytical solutions of the Zabolotskaya–Khokhlov (ZK) equation, which describes the propagation of nonlinear acoustic waves with diffraction effects in a medium. Its physical significance lies in modeling the behavior of high-amplitude sound waves, where nonlinear effects (such as wave steepening) and diffraction (spreading of the wave in directions perpendicular to the main propagation axis) both play an important role. In the ZK equation, time derivatives are described in terms of conformable derivatives, which have gained popularity recently and have drawn attention from numerous studies. It offers nearly all the fundamental characteristics of the classical derivative in the Newtonian style, and it looks into the precise solution of the mathematical model this derivative expresses. Also sub-equation method is used as a tool for obtaining the analytical results. 3D graphical illustrations are given to express the physical behavior of obtained results.

Keywords

Analytical solution, Conformable fractional derivative, Fractional calculus, Nonlinear acoustics

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