title: A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).
abstract: A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.
authors.affiliation: Department of Informatics, University of Oslo, P.O. Box 1080, NO-0316 Oslo, Norway. fabrice@ifi.uio.no
authors.forename: Fabrice
authors.initials: F
authors.lastname: Prieur
authors.forename: Gregory
authors.initials: G
authors.lastname: Vilenskiy
authors.forename: Sverre
authors.initials: S
authors.lastname: Holm
mesh_terms: D000162:Acoustics; D055119:Elastic Modulus; D019277:Entropy; D009038:Motion; D017711:Nonlinear Dynamics; D011312:Pressure; D013016:Sound; D013314:Stress, Mechanical; D013816:Thermodynamics