Abstract Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry are studied by use the Green–Naghdi (GN) equations in three dimensions. A numerical wave tank consisting deep, transitional, regions is created. Various forms three-dimensional bathymetry, ramps with nonuniform profiles large slopes, used connect deep-water side shelf. wavemaker placed at upwave domain...

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre–Green–Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not...

Abstract In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, present magnetic analogue 2D Green–Naghdi water waves under a weak pressure assumption presence weakly sheared vorticity and currents. Our meth...