The evolution of strongly dispersive internal solitary waves (ISWs) over slope-shelf topography is studied in a two-layer system of finite depth. We consider the high-order vmeKdV model extending the Korteweg-de Vries (KdV) equation with coupling terms of [Formula: see text] order to treat the strong dispersion in the problem which has variable coefficients to adapt the varying bottom topography. The strongly dispersive initial ISW is characterized by the meKdV equation according to the comparison with experiments and can be propagated by the vmeKdV equation according to the comparison between vmeKdV and vKdV theories. The vmeKdV equation is numerically implemented adopting the finite difference scheme. Three dimensionless ISW amplitudes [Formula: see text], 1.136, 1.41 and two slope inclinations [Formula: see text], 1/10 are considered. The deformation of the ISW is observed when a wave propagates past over the slope. The balancing of shoaling effect and energy dispersion determine the amplitude variation. In the cases of mild or steeper slopes, the terminal wave has a stable profile and amplitude, commonly consistent to the meKdV profile with smaller amplitude. In a particular case of mild slope with very small initial amplitude, the terminal wave amplitude grows larger than the original value.
An Evans-function approach to spectral stability of internal solitary waves in stratified fluids