The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, optics, and other fields. In the process studying these topics, very obtain exact solutions equation. this paper, a general Riccati treated as an auxiliary equa...

This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...

The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material.  The freque...

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point...

An unsteady fully three-dimensional model of Lake Binaba (a shallow small reservoir) in semi-arid Upper East Region of Ghana has been developed to simulate its temperature dynamics. The model developed is built on the Reynolds Averaged Navier–Stokes (RANS) equations, utilizing the Boussinesq approach. As the results of the model are significantly affected by the physical conditions on the bound...

The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak nonlinearity, we derive a Nonlinear Schroedinger equation to describe the envelope of the wave packet. We find that nonlinearity has a ...

With the aid of symbolic computation, a new extended Jacobi elliptic function expansionmethod is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function s...

with the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. many site-specific methods have been proposed for modeling indoor radio channels. among these methods, the ray tracing algorithm and the finite-difference time domain (fdtd) method are the most popular ones. the ray tracing approach ...

The acoustic ducting effect by curved nonlinear gravity waves in shallow water is studied through idealized models in this paper. The internal wave ducts are three-dimensional, bounded vertically by the sea surface and bottom, and horizontally by aligned wavefronts. Both normal mode and parabolic equation methods are taken to analyze the ducted sound field. Two types of horizontal acoustic mode...

The three-dimensional problem of wave trapping above a submerged round sill was first analysed by Longuet-Higgins on the basis of a linear shallow-water theory. The large responses predicted by the theory were, however, not well borne out by the experiments of Barnard, Pritchard & Provis, and this has motivated a more detailed study of the problem. A full linear theory for both inviscid and wea...