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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1059–1091 | Cite as

Solitary Wave Solutions to a Class of Modified Green–Naghdi Systems

  • Vincent Duchêne
  • Dag Nilsson
  • Erik Wahlén
Open Access
Article
  • 136 Downloads

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 Duchêne et al. (Stud Appl Math 137:356–415, 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.

Notes

Acknowledgements

V. Duchêne was partially supported by the Agence Nationale de la Recherche (project ANR-13-BS01-0003-01 DYFICOLTI). D. Nilsson and E. Wahlén were supported by the Swedish Research Council (Grant No. 621-2012-3753).

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.IRMAR - UMR 6625University of Rennes 1, CNRSRennesFrance
  2. 2.Centre for Mathematical SciencesLund UniversityLundSweden

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