Solitary Wave Solutions to a Class of Modified Green-Naghdi Systems
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.
- Publication:
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Journal of Mathematical Fluid Mechanics
- Pub Date:
- September 2018
- DOI:
- arXiv:
- arXiv:1706.08853
- Bibcode:
- 2018JMFM...20.1059D
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- J. Math. Fluid Mech. 20(3), pp. 1059-1091 (2018)