On multisolitonic decay behavior of internal gravity waves
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.