The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and Complete discrimination system for polynomial we obtained classification of travelling patterns. Among those patterns, new singular patterns double periodic first time. And draw graphs help us to understand dynamics behaviors intuitionally.

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For wider class relaxation functions, We show that dissipation produced memory eect strong enough to produce general decay results. establish results, from which usual exponential polynomial rates are only special cases.

We study the behavior in time of solutions to several systems equations for porous-thermo-elastic problems when one variables is considered be quasi-static or, other words, whose second derivative can neglected. analyze three different situations using classical Fourier law and also type II or III Green–Naghdi heat conduction models.

The present paper is devoted to the determination of displacement, stresses and temperature from three dimensional anisotropic half spaces due to presence of heat source. The normal mode analysis technique has been used to the basic equations of motion and generalized heat conduction equation proposed by Green-Naghdi model-II [1]. The resulting equation are written in the form of a vector –matr...

The main objective of this work is to study the homogeneous thermoelastic interactions in an isotropic hollow thin cylinder immersed electric–magnetic field using linear Moore–Gibson–Thompson theory thermoelasticity, taking into account generalized Ohm’s law. MGT system equations for new model created by incorporating a relaxation period Green–Naghdi type III framework. In addition, Maxwell tha...

We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in context of nonlinear dynamics surface water waves under wind forcing, finite depth. The anti-dissipation occurs du to continuos transfer energy wave. find solitary wave solution system, with an increasing amplitude action. This leads blow-up time for infinitely large asymptotic space. dispersive, anti-dissipative and fully phe...

A study is made of the propagation of time-harmonic magneto-thermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of Kelvin-Voigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The generalized thermoelasticity theory of type II (Green and Naghdi model) is used to study the propagat...