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New exact solutions of nonlinear fractional acoustic wave equations in ultrasound

机译：超声中非线性分数声波方程的新精确解

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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. (C) 2016 Elsevier Ltd. All rights reserved.
机译：在本文中，设计了分数阶非线性声波方程的新精确解。通过第一积分方法获得了分数阶Burgers-Hopf方程和Khokhlov-Zabolotskaya-Kuznetsov（KZK）方程的行进周期波解。发现非线性超声建模在医疗和工业领域都有越来越多的应用，在这些领域中，由于高压振幅，非线性传播的影响不再可以忽略。考虑到非线性影响，超声束分析在这些应用中使精度更高。 Burgers-Hopf方程是数学物理学中广泛研究的模型之一。另外，KZK抛物线非线性波方程是在耗散介质中传播3D衍射声束的最广泛使用的非线性模型之一。在目前的分析中，这些非线性方程已通过第一积分法求解。结果，这些分数阶声波方程式首次获得了新的精确解析解。以图形方式显示了获得的结果，以证明该方法的有效性。 （C）2016 Elsevier Ltd.保留所有权利。

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