Abstract “Green — Naghdi Theory, Part A: Green (GN) Equations for Shallow Water Waves” have investigated the linear dispersion relations of high-level GN equations in shallow water. In this study, deep water waves are investigated. traditional waves, velocity distribution assumption involves only one representative wave number. Herein, a new shape function with multiple numbers is employed. Fur...

the three-phase-lag model and green–naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field.  the modulus of the elasticity is given as a linear function of the reference temperature. the exact expressions ...

Article history: Received 4 March 2012 Received in revised form 14 September 2012 Accepted 17 September 2012 Available online xxxx

ABSTRAC: The present paper deals with the review on the development of the theory of two-temperature thermoelasticity. The basic equations of two-temperature thermoelasticityin context of Lord and Shulman [6] theory and Green and Naghdi[15] theories of generalized thermoelasticity are reviewed. Relevant literature on two-temperature thermoelasticity is also reviewed.

Vertical averaging of the three dimensional incompressible Euler equations leads to several reduced dimension models of ow over topography, including the one-layer and two-layer classic shallow water equations, and the one-layer and two-layer nonhydrostatic Green-Naghdi equations. These equations are derived and their well-posedness is discussed. Several implicit and explicit nite diierence app...

By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green–Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric rep...

We consider here the 1D Green-Naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves. We show that the solution of the Green-Naghdi equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition.

We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1 + 1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom and a rigid lid. These models are tailored to improve the frequency dispersion of the original bi-layer Green-Naghdi model, and in particular to manage high-...