Representation of the absorption of nonlinear waves by fractional derivatives

Abstract

Fractional derivatives of arbitrary order are incorporated into a model nonlinear equation in order to simulate the absorption mechanism in a finite frequency domain. That makes it possible to take into account a power dependence of the absorption coefficient on the frequency at any real degree. The model gives a mathematical description of a large set of well‐known absorption mechanisms. The method is applied to calculate weakly nonlinear oscillations in a nonrigid tube. As a result, the value of the absorption coefficient and its dependence on the frequency are found based on experimental data.