A note on acoustic propagation in power-law fluids: Compact kinks, mild discontinuities, and a connection to finite-scale theory

Acoustic traveling waves in a class of power-law viscosity fluids are investigated. Both bi-directional and unidirectional versions of the one-dimensional (1D), weakly non-linear equation of motion are derived; traveling wave solutions (TWSs), special cases of which take the form of compact and algebraic kinks, are determined; and the impact of the bulk viscosity on the structure/nature of the kinks is examined. Most significantly, we point out a connection that exists between the power-law model considered here and the recently introduced theory of finite-scale equations.