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

Vincent Duchêne (1) , Dag Nilsson (2) , Erik Wahlén (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Centre for Mathematical Sciences

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, 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.

Mots clés: Solitary waves; Gravity waves; Internal waves; Green-Naghdi system

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Duchêne, Dag Nilsson, Erik Wahlén. Solitary wave solutions to a class of modified Green-Naghdi systems. Journal of Mathematical Fluid Mechanics, 2018, 20 (3), pp.1059-1091. ⟨10.1007/s00021-017-0355-0⟩. ⟨hal-01548404⟩