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.
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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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Duchêne, V., Nilsson, D. & Wahlén, E. Solitary Wave Solutions to a Class of Modified Green–Naghdi Systems. J. Math. Fluid Mech. 20, 1059–1091 (2018). https://doi.org/10.1007/s00021-017-0355-0
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DOI: https://doi.org/10.1007/s00021-017-0355-0