Solitary wave solutions to a class of modified Green-Naghdi systems
Analysis of PDEs
2021-10-01 v1
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.
Keywords
Cite
@article{arxiv.1706.08853,
title = {Solitary wave solutions to a class of modified Green-Naghdi systems},
author = {Vincent Duchêne and Dag Nilsson and Erik Wahlén},
journal= {arXiv preprint arXiv:1706.08853},
year = {2021}
}