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...

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

In this paper, we present a new non-linear dispersive model for open channel and river flows. These equations are the second-order shallow water approximation of section-averaged (three-dimensional) incompressible irrotational Euler system. This asymptotic generalises well-known one-dimensional Serre–Green–Naghdi (SGN) rectangular section on uneven bottom to arbitrary channel/river section.

The present paper deals with a modified Serre–Green–Naghdi (mSGN) system that has been introduced by Clamond et al. (2017) to improve the dispersion relation. We precise blow-up scenario of mSGN equations and we prove existence class solutions develop singularities in finite time. All presented results hold, same proof, for surface tension.