Related papers: Wavelet-based integral representation for solution…
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…
We demonstrate that wavelet bases have features that make them advantageous for solving momentum-space scattering integral equations. Using the example of two nucleons interacting with the Malfliet-Tjon V interaction, we show it is possible…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…
This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence of classical solutions of semilinear wave equations in one…
For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give…
This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well.…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
In this paper we will argue that the superposition of waves can be calculated and taught in a simple way. We show, using the Gauss's method to sum an arithmetic sequence, how we can construct the superposition of waves - with different…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of…
In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do…