Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth

Abstract

Solitary internal waves in stratilied fluids of finite depth are investigated. Using a general criterion for the stability of travelling-wave solutions of one-dimensional nonlinear long-wave models and ideas from the theory of totally positive operators, the stability of the solitary-wave solutions of the intermediate long-wave equation is demonstrated. In the process of carrying out this programme of research, new general results are obtained that bear upon the stability of solitary-wave solutions of a class of model equations of the Korteweg-de Vries type that govern approximately the evolution of small-amplitude long waves.