Existence of solitary waves solutions for internal waves in two-layers systems

TL;DR

This paper proves the existence of solitary wave solutions in two-layer internal wave models, specifically for Boussinesq-Full dispersion, ILW, and BO systems, advancing understanding of internal wave dynamics.

Contribution

It establishes the existence of solitary waves for multiple two-layer internal wave models, including Boussinesq-Full dispersion, ILW, and BO systems, which was previously unconfirmed.

Findings

Existence of solitary waves for Boussinesq-Full dispersion system.

Existence of solitary waves for ILW system.

Existence of solitary waves for BO limit system.

Abstract

The aim of this paper is to establish the existence of solitary wave solutions for two classes of two-layers systems modeling the propagation of internal waves. More precisely we will consider the Boussinesq-Full dispersion system and the Intermediate Long Wave (ILW) system together with its Benjamin-Ono (BO) limit.