A theoretical model for internal solitary waves for stratification consisting of two
layers of incompressible fluid with a constant Brunt–Väisälä frequency and a density
jump at the boundary between layers (‘2.5-layer model’) is presented. The equation
of motion for solitary waves in the case of a constant Brunt–Väisälä frequency N
is linear, and nonlinearity appears due only to boundary conditions between layers.
This allows one to obtain in the case of long waves a single ordinary differential
equation for an internal solitary wave profile. In the case of nearly homogeneous
layers the solitons obtained here coincide with the solitons calculated by Choi &
Camassa (1999), and in the weakly nonlinear case they reduce to KdV solitons. In the
general situation strong 2.5-layer solitons can correspond to higher modes. Sufficiently
strong solitons could also possess a recirculating core (at least, as a formal solution).
The model was applied to the data collected during the COPE experiment. The
results are in reasonable agreement with experimental data.