We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre–Green–Naghdi system; it describes future states free depth averaged horizontal velocity, given their initial state. The lack knowledge velocity field well provided measurements lead to an ill-posed problem that cannot be solved traditional techniques. To this end...

We present a study of the physical characteristics traveling waves at shallow and intermediate water depths. The main subject is to influence nonlinearity on dispersion properties waves, their limiting heights steepness, shape solitary etc. A fully nonlinear Serre–Green–Naghdi-type model, classical weakly Boussinesq model fifth-order Stokes wave solutions were chosen as models for comparison. a...

The first complete linear theory, based on Kirchhoff’s [1850] earlier works on plates, was given by Love [1888]. The modern theory (linear and nonlinear) comes from the works by Naghdi and Koiter in the sixties. In such models the displacement variables are functions defined on the mean surface and the resulting equations are differential equations on a smooth 2-dimensional submanifold of the t...

This research aims to investigate photo-thermoelastic interactions in a rotating infinite semiconducting solid cylinder under high magnetic field acting along its axis with the Hall current effect. The boundary surface is subjected variable heat flux generated by an exponential laser pulse. governing equations are expressed using new model generalized Moore–Gibson–Thompson photo-thermal (MGTPT)...

In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-Naghdi (SGN) equations describing shallow water flows, and Iordanskii-Kogarko-Wijngaarden (IKW) fluids containing small compressible gas bubbles. These models are Euler-Lagrange for a given Lagrangian share common mathematical structure, namely dependence of pressure on material derivatives macroscopic var...

Abstract This article develops a non-cooperative game with managerial quantity-setting firms in which owners choose whether to delegate output and abatement decisions managers through contract based on emissions (conventionally denoted as ‘green’ delegation, GD) instead of sales (sales SD), the government levies an tax incentivise firms’ emissions-reduction actions. First, it compares Nash equi...