2015/03/11 by Yoshimasa Matsuno · 35 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Coastal and Marine Dynamics #Hamiltonian (control theory) #Hamiltonian system #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Ocean Waves and Remote Sensing #Perturbation (astronomy) #Physics #Quantum mechanics #Wave equation #nlin.SI
paper · pdf · doi:10.1016/j.physd.2015.03.001
published in Physica D Nonlinear Phenomena 301-302, 1-7 (Elsevier BV) · 21 pages
openalex publication_date 2015/03/11 · arxiv created 2015/03/30 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A novel method is developed for extending the Green-Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.