A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

We study the action of elementary shift operators on spherical functions on ordered symmetric spaces ${ℳ}_{m,n}$ of Cayley type, where $m\in \mathbb{N}$ denotes the multiplicity of the short roots and $n\in \mathbb{N}$ the rank of the symmetric space. For $m$ even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on ${ℳ}_{m,n}$ by a reduction to the rank 1 case. Finally we generalize our notions and results to $B{C}_n$ type root systems.