  We claim that changes of scales and fine-structure could increase from
multisoliton behavior of internal waves dynamics and, further, in the so-called
"wave mixing". We consider initial-boundary problems for Euler equations with a
stratified background state that is valid for internal water waves. The
solution of the problem we search in the waveguide mode representation for a
current function. The orthogonal eigenfunctions describe a vertical shape of
the internal wave modes and satisfy a Sturm-Liouville problem for the vertical
variable. The Cauchy problem is solved for initial conditions with realistic
geometry and magnitude. We choose the geometry and dimensions of the McEwan
experiment with the stratification of constant buoyancy frequency. The
horizontal profile is defined by numerical solutions of a coupled Korteweg-de
Vries system. The numerical scheme is proved to be convergent, stable and
tested by means of explicit solutions for integrable case of the system.
Together with the solution of the Sturm-Liouville problem it gives the complete
internal waves profile.
