On the Propagation of Finite-Amplitude Acoustic Waves in Mono-Relaxing Media

The propagation of finite-amplitude acoustic traveling waves in a class of mono-relaxing media is considered. The resulting associated ordinary differential equation (ODE), which is of the Abel type, is analyzed and exact, approximate, and asymptotic solutions are derived. In addition, numerical simulations are presented, special cases are discussed, and connections to other fields are noted. The analysis carried out here also serves to highlight some of the many applications of Abel's equation and the Lambert W-function, a relatively recent addition to the family of special functions, in the physical sciences.