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.