The ocean flow in equatorial regions

is complicated due to stratification (with

lower-density fluid overlying an abyssal fluid

region that is practically motionless at great

depths) and to the presence of underlying currents

with flow-reversal. Gravity water waves occur at

the surface, while large internal waves propagate

as oscillations of the thermocline (the interface

separating the two layers of different constant

density). We will discuss the development of a

Hamiltonian approach to gain insight into the

nonlinear dynamics of equatorial wave-current

interactions. Of special interest are the observed

equatorial solitary-like waves (localised waves that

maintain their coherence, propagating with constant

speed and unaltered shape) since these wave

patterns are not captured by linear theory. A

Hamiltonian formulation of the governing equations

leads to structure-preserving (and even

structure-enhancing) models in the weakly nonlinear

shallow-water regime, thus opening up new possibilities

for in-depth studies. In particular, an observed

behaviour of internal waves that is reminiscent of

soliton theory -- large waves that occur in wave packets

and disintegrate into trains of solitary waves, with

the distances between the waves, and their amplitudes,

decreasing from front to rear -- is of interest.