  We derive a new hyperbolic model describing the propagation of internal waves
in a stratified shallow water with a non-hydrostatic pressure distribution. The
construction of the hyperbolic model is based on the use of additional
`instantaneous' variables. This allows one to reduce the dispersive multi-layer
Green--Naghdi model to a first-order system of evolution equations. The main
attention is paid to the study of three-layer flows over uneven bottom in the
Boussinesq approximation with the additional assumption of hydrostatic pressure
in the intermediate layer. The hyperbolicity conditions of the obtained
equations of three-layer flows are formulated and solutions in the class of
travelling waves are studied. Based on the proposed hyperbolic and dispersive
models, numerical calculations of the generation and propagation of internal
solitary waves are carried out and their comparison with experimental data is
given. Within the framework of the proposed three-layer hyperbolic model, a
numerical study of the propagation and interaction of symmetric and
non-symmetric soliton-like waves is performed.
