New exact solutions of nonlinear fractional acoustic wave equations in ultrasound

Abstract

In this paper, new exact solutions of fractional nonlinear acoustic wave equations have been devised. The travelling periodic wave solutions of fractional Burgers–Hopf equation and Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation have obtained by first integral method. Nonlinear ultrasound modelling is found to have an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible. Taking nonlinear effects into account, the ultrasound beam analysis makes more accurate in these applications. The Burgers–Hopf equation is one of the extensively studied models in mathematical physics. In addition, the KZK parabolic nonlinear wave equation is one of the most widely employed nonlinear models for propagation of 3D diffraction sound beams in dissipative media. In the present analysis, these nonlinear equations have solved by first integral method. As a result, new exact analytical solutions have been obtained first time ever for these fractional order acoustic wave equations. The obtained results are presented graphically to demonstrate the efficiency of this proposed method.