The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.    

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave-equation traveltime inversion (WT), seismograms are computed by any full-wave forward modeling method (we use a finitedifference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a leas...

The wave maps equation has become a very popular topic in recent years. The aim of these expository notes is to present a non-technical survey of the ideas and methods which have proved useful in the study of wave maps, leading up to the latest results. The remaining open problems are also stated and explained.

The main goal of this paper is to develop a “wave equation” for graphs that is very similar to the wave equation utt = ∆u in analysis. Whenever this type of wave equation is involved in a result in analysis, our graph theoretic wave equation seems likely to provide the tool to link the result in analysis to an analogous result in graph theory. Traditional graph theory defines a Laplacian, ∆, as...

Let L be the distinguished Laplacian on certain semidirect products of R by R which are of ax+ b-type. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators of the form e √ ψ( √ L/λ) for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ ≤ 1 and supported in [1, 2] if λ ≥ 1. As corollary, we reprove a basic...

This is a note for the lectures given on Oct. 21st and 23rd, 2014 in lieu of D. Tataru, for the course MAT222 at UC Berkeley. 1. Wave equation The purpose of these lectures is to give a basic introduction to the study of linear wave equation. Let d ≥ 1. The wave operator, or the d’Alembertian, is a second order partial differential operator on R defined as (1.1) := −∂ t + ∂ x1 + · · ·+ ∂ xd = −...

The wave-equation wavefront migration (WWM) is a potentially efficient form of wave equation migration, where the finite-difference stencil is only applied around the leading portion of the wavefront. WWM has the accuracy of wave-equation migration, fewer aliasing and migration artifacts, and can potentially be much faster than the standard reverse-time migration. The potential drawbacks are th...

Spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero-offset experiment, and the data are seismic data after normal moveout (NMO). The formulation of the (linear) relation between the data and the model is based on the wave equation and on Fourier analysis of aliasing. A processing se...

‎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 thomas-fermi (tf) equation has proved to beuseful for the treatment of many physical phenomena. in this pa-per, the traveling wave solutions of the kdv equation is investi-gated by the simplest equation method. also, the effect of differentparameters on these solitary waves is considered. the numericalresults is conformed the good accuracy of presented method.