Anomalous propagation of acoustic traveling waves in thermoviscous fluids under the Rubin–Rosenau–Gottlieb theory of dispersive media

• Nonlinear acoustic waves in thermoviscous fluids are examined under RRG theory.
• A nonlinear version of the van Wijngaarden–Eringin equation is derived.
• An exact traveling wave solution in the form of a kink is determined.
• The existence of an anomaly in the kink’s wave speed is established.
• Possible explanations of the anomaly are noted.

We report on an apparent anomaly associated with the compressible, thermoviscous version of what has come to be known as RRG theory. The difficulty in question, which does not appear to impact the lossless special case of this theory, manifests itself under the traveling wave assumption and has the shock-front of the resulting kink waveform and the (instigating) piston propagating in opposite directions.