The object of this article is the comparison of numerical solutions of the so-called Whitham equation describing wave motion at the surface of a perfect fluid to numerical approximations of solutions of the full Euler free-surface water-wave problem. The Whitham equation ηt + 3 2 c0 h0 ηηx +Kh0∗ ηx = 0 was proposed by Whitham [33] as an alternative to the KdV equation for the description of sur...

This tutorial describes mixed-domain wave-equation migration and migration velocity analysis techniques in a unified theoretical framework. I review two of the most general mixed-domain migration methods, Fourier finite-difference and generalized screen, and show how other commonly used wave-equation migration methods come about as special cases. I use the Born approximation to derive general e...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

we will present a detailed investigation of intersubband transitions process in core-multi shells quantum dots. the confined wave functions and eigenenergies of electrons in quantum dots have been calculated under the effective-mass approximation by solving a three-dimensional schrodinger equation. excellent dependence is found between size effects, time relaxation and degenerate four wave mixi...

It is known that von Neumann-Landau wave equation can present a mathematical formalism of motion of quantum mechanics, that is an extension of Schrödinger's wave equation. In this paper, we concern with the Dirichlet problem of the stationary von Neumann-Landau wave equation: where Ω is a bounded domain in R n. By introducing anti-inner product spaces, we show the existence and uniqueness of th...

In this note, we use an elementary argument to show that the existence and unitarity of radiation fields implies asymptotic partition of energy for the corresponding wave equation. This argument establishes the equipartition of energy for the wave equation on scattering manifolds, asymptotically hyperbolic manifolds, asymptotically complex hyperbolic manifolds, and the Schwarzschild spacetime. ...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

The 11-parameter transformation group with generators (2) and (5) is called the extended Poincaré group P̃ (1, 3). The above result admits the following group-theoretical interpretation: on the set of solutions of the nonlinear wave equation (1) two inequivalent representations of the extended Poincaré group are realized. Each representation gives rise to a P̃ (1, 3)nonlinear wave equation with a...

This article is an introduction to wave equations, emphasizing for simplicity the case of a single space dimension. What we mean by a wave equation will gradually be made more precise as we proceed, but at first, we will just a mean a certain kind of ordinary differential equation on the space C∞(Rn, V ), where V is some finite dimensional vector space, usually R or C, (and generally we will ta...