Transmission and reflection of an internal solitary wave on a two-laye
r fluid as it encounters a barrier is considered. An edge-layer theory
is used to derive the reduced boundary conditions relevant to the sha
llow-water equations. It is found that for a moderate height of the ba
rrier the incident wave is not affected except by being phase shifted.
On the other hand, for a relatively high barrier the incident wave sp
lits into a transmitted wave and a reflected wave. The reflected wave
evolves into a small soliton with decaying ripples, and the transmitte
d wave evolves into a larger soliton and an oscillating tail.