title: Nonlinear acoustic wave equations with fractional loss operators.
abstract: Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
authors: Department of Informatics, University of Oslo, P.O. Box 1080, NO-0316 Oslo, Norway. fabrice@ifi.uio.no
authors: Fabrice
authors: F
authors: Prieur
authors: Sverre
authors: S
authors: Holm
mesh_terms: D000162:Acoustics; D055119:Elastic Modulus; D019277:Entropy; D005583:Fourier Analysis; D009038:Motion; D017711:Nonlinear Dynamics; D013016:Sound; D013314:Stress, Mechanical; D013814:Thermal Conductivity; D013997:Time Factors; D014783:Viscosity