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 Duch{ê}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.

References in corpus (1)

• A new class of two-layer Green-Naghdi systems with improved frequency dispersion

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• Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
• The existence and decay of solitary waves for the Fornberg-Whitham equation