  In this announcement, we report results on the existence of families of
large-amplitude internal hydrodynamic bores. These are traveling front
solutions of the full two-phase incompressible Euler equation in two
dimensions. The fluids are bounded above and below by flat horizontal walls and
acted upon by gravity. We obtain continuous curves of solutions to this system
that bifurcate from the trivial solution where the interface is flat. Following
these families to the their extreme, the internal interface either overturns,
comes into contact with the upper wall, or develops a highly degenerate "double
stagnation" point.
  Our construction is made possible by a new abstract machinery for global
continuation of monotone front-type solutions to elliptic equations posed on
infinite cylinders. This theory is quite robust and, in particular, can treat
fully nonlinear equations as well as quasilinear problems with transmission
boundary conditions.
