# Solitary wave solutions to a class of modified Green-Naghdi systems

## TL;DR

This paper establishes the existence and describes the asymptotic behavior of solitary wave solutions in a modified Green-Naghdi system, which better models long surface or internal waves with improved dispersion properties.

## Contribution

It introduces a new class of modified Green-Naghdi systems and constructs solitary wave solutions using a constrained minimization approach involving complex non-local operators.

## Key findings

- Existence of solitary wave solutions is proven.
- Asymptotic behavior of solutions is characterized.
- The modified system improves dispersion modeling.

## Abstract

We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green-Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duch{\^e}ne, Israwi and Talhouk (Stud. Appl. Math.,137 (2016)) in order to improve the frequency dispersion of the original Green-Naghdi system while maintaining the same precision. The solitary waves are constructed from the solutions of a constrained minimization problem. The main difficulties stem from the fact that the functional at stake involves low order non-local operators, intertwining multiplications and convolutions through Fourier multipliers.