Abstract
Working in the context of poroacoustics, we present new, physically relevant, explicit solutions to the Cauchy problem for the model we term the (1D) damped Riemann equation. The solitary waveforms that evolve from both Lorentzian (C∞-smooth) and symmetric-exponential (C0-smooth) initial conditions are analyzed, the focus being on wave overturning and the evolution/structure of the shocks which develop thereafter. In addition to those for both the multi- and single-valued forms of each solution, expressions for the shock amplitude, velocity, and critical values of the physical parameters are derived/compared. Lastly, links to other areas of continuum physics, and possible follow-on investigations, are noted.
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