  Stationary expansion shocks have been recently identified as a new type of
solution to hyperbolic conservation laws regularized by non-local dispersive
terms that naturally arise in shallow-water theory. These expansion shocks were
studied in (El, Hoefer, Shearer 2016) for the Benjamin-Bona-Mahony equation
using matched asymptotic expansions. In this paper, we extend the analysis of
(El, Hoefer, Shearer 2016) to the regularized Boussinesq system by using
Riemann invariants of the underlying dispersionless shallow water equations.
The extension for a system is non-trivial, requiring a combination of small
amplitude, long-wave expansions with high order matched asymptotics. The
constructed asymptotic solution is shown to be in excellent agreement with
accurate numerical simulations of the Boussinesq system for a range of
appropriately smoothed Riemann data.
