Every (1 polarization) cylindrical wave solution of vacuum general relativity is completely determined by a corresponding axisymmetric solution to the free scalar wave equation on an auxilliary 2+1 dimensional flat spacetime. The physical metric at radius R is determined by the energy, γ(R), of the scalar field in a box (in the flat spacetime) of radius R. In a recent work, among other importan...

In this article, with the aid of Maple software, exact solutions to space-time fractional symmetric regularized long wave (SRLW) equation are successfully examined by G ? / 2 -expansion and extended complex methods. Consequen...

The main goal of the current work is to develop numerical approaches that use Yang transform, homotopy perturbation method (HPM), and Adomian decomposition analyze fractional model regularized long-wave equation. shallow-water waves ion-acoustic in plasma are both explained by first combines transform with He’s polynomials. In contrast, second polynomials method. Caputo sense applied derivative...

In this paper we investigate the pseudoparabolic equation ∂tc = div { k (c) μ ( − P ′ C (c)∇c + τ∇∂tc + gρen )} , where τ is a positive constant, c is the moisture content, k is the hydraulic conductivity and PC is the static capillary pressure. This equation describes unsaturated flows in porous media with dynamic capillary pressure saturation relationship. In general, such models arise in a n...

This dissertation addresses the problem of interpolating irregularly spaced seismic exploration data to regular spatial locations. This problem arises in practice in three-dimensional seismic exploration in such applications as Kirchhoff prestack migration, multiple elimination, waveequation migration, and 4-D seismic monitoring. I formulate data regularization as a linear-estimation problem an...

This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial...

The regularized long-wave or BBM equation ut + ux + uux − uxxt = 0 was derived as a model for the unidirectional propagation of long-crested, surface water waves. It arises in other contexts as well, and is generally understood as an alternative to the Korteweg-de Vries equation. Considered here is the initial-value problem wherein u is specified everywhere at a given time t = 0, say, and inqui...