On a nonlocal Boussinesq system for internal wave propagation

TL;DR

This paper studies a nonlocal Boussinesq system modeling internal wave propagation in a two-layer fluid, focusing on well-posedness and solitary wave solutions under a rigid lid assumption.

Contribution

It investigates the well-posedness of the Cauchy problem and the existence and properties of solitary wave solutions for this specific nonlocal Boussinesq system.

Findings

Established well-posedness conditions for the system

Proved existence of solitary wave solutions

Analyzed properties of these solitary waves

Abstract

In this paper we are concerned with a nonlocal system to model the propagation of internal waves in a two-layer interface problem with rigid lid assumption and under a Boussinesq regime for both fluids. The main goal is to investigate aspects of well-posedness of the Cauchy problem for the deviation of the interface and the velocity, as well as the existence of solitary wave solutions and some of their properties.