On the Existence of Solitary Waves for an Internal System of the Benjamin–Ono Type

Abstract

We derive a Benjamin–Ono type system with high dispersion to describe the propagation of internal waves in the case of wave speed large enough. We also establish the existence of solitary wave solutions for the Benjamin–Ono type system, by adapting the positive operator theory in a cone on Frechet spaces introduced originally by Krasnosel’skii and by using Tuck’s Result (everywhere-convex functions have everywhere-positive Fourier-cosine transforms) to guarantee the positiveness of the kernels involved in the fixed point setting.