Instability analysis of internal solitary waves in a nearly uniformly stratified fluid

Long finite-amplitude internal solitary waves propagating in a stratified fluid with nearly uniform stratification are considered within an asymptotic approximation leading to a nonlocal evolution equation of the Korteweg–de Vries (KdV) type. Analytical properties of this equation and its solitary wave solutions are studied and a criterion for solitary wave instability is derived. This criterion coincides with that for solitary waves in a local generalized KdV equation. Applications of these results reveal that strengthening of the stratification might lead to destabilization of smooth solitary waves and their blow-up into vortex-type wave structures.