Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...

Soliton interactions for the extended Korteweg-de Vries (KdV) equation are examined. It is shown that the extended KdV equation can be transformed (to its order of approximation) to a higher-order member of the KdV hierarchy of integrable equations. This transformation is used to derive the higher-order, two-soliton solution for the extended KdV equation. Hence it follows that the higher-order ...

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both rightand left-moving wa...

[1] The tidal flow field in a basin of small dimensions with respect to the tidal wavelength is calculated. Under these conditions, the tide becomes a standing wave oscillating synchronously (with a flat water surface) over the whole basin. The shallow water equations can thus be strongly simplified, expressing the discharge vector field in terms of a potential function and a stream function. T...

The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative fini...

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 ...

We solve the Cauchy problem for the n-dimensional wave equation, where n is an odd integer, using elementary properties of the Fourier transform. We also show that the solution can be obtained by invoking Bessel functions. The wave equation has a rich history fraught with controversy, both mathematical, see [9], and physical, see [16]. It all started in 1747 when d’Alembert, in a memoir present...

The successful implementation of a finite element model for computing shallow-water flow requires the identification and spatial discretization of a surface water region. Since no robust criterion or node spacing routine exists, which incorporates physical characteristics and subsequent responses into the mesh generation process, modelers are left to rely on crude gridding criteria as well as t...

This research focusses on the facies distribution, paleoenvironment and paleoecology of the foraminifera of the Guri Member in the northern Bandar Abbas Hinterland located in the Roydar area of southern Iran. The Guri Member is 570 meters thick and composed of limestone, argillaceous limestone and marl. The distribution of the foraminifera in the study area indicates the existence of three bioz...