In this paper, we look at the propagation of internal solitary waves over three
different types of slowly varying region, i.e. a slowly increasing slope, a smooth bump and
a parabolic mound in a two-layer fluid flow. The appropriate mathematical model for this
problem is the variable-coefficient extended Korteweg-de Vries equation. The governing
equation is then solved numerically using the method of lines. Our numerical simulations
show that the internal solitary waves deforms adiabatically on the slowly increasing slope.
At the same time, a trailing shelf is generated as the internal solitary wave propagates
over the slope, which would then decompose into secondary solitary waves or a wavetrain.
On the other hand, when internal solitary waves propagate over a smooth bump or a
parabolic mound, a trailing shelf of negative polarity would be generated as the results of
the interaction of the internal solitary wave with the decreasing slope of the bump or the
parabolic mound. The secondary solitary waves is observed to be climbing the negative
trailing shelf.