The geometric optics approximation to high frequency anisotropic wave propagation reduces the anisotropic wave equation to a static Hamilton–Jacobi equation. This equation is known as the anisotropic eikonal equation and has three different coupled wave modes as solutions. We introduce here a level set-based Eulerian approach that captures all three of these wave propagations. In particular, ou...

A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are nece...

Often in the history of physics a guiding line of mathematical thought has permeated the whole of the science for years, tying together apparently unrelated branches of the subject, contributing to the unity of physics, but at the same time stimulating philosophical thought, and focussing attention on a branch of mathematics, and leading to its development. The Newtonian mechanics was such a gu...

We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved quantity which looks like helicity. The principle of superposition is retained in a slightly altered manner. External potentials can be introduced in a way th...

In this paper, we give the quantum wave equations of single photon when it is in the free or medium space. With these equations, we can study light interference and diffraction with quantum approach. Otherwise, they can be applied in quantum optics and photonic crystal. PACS number(s): 03.65.-w, 42.50.Ar, 42.50.Dv

16 [16] S. Mallat Multiresolution approximation and wavelet orthonormal bases of L 2 (R) Transactions of AMS. vol 135 (1989) [17] K.J. Marfurt Accuracy of nite-dierence and nite-element modeling of the scalar wave equation. [21] V. Perrier & C. Basdevant La d ecomposition en ondelettes p eriodiques, un outil pour l'analyse de champs inhomog enes. Th eorie et algorithmes. La Recherche A erospati...

The main result of this paper is a generalization of the property that, for smooth u, uxy = 0 implies (*) u(x, y) = a(x) + b(y). Any function having generalized unsymmetric mixed partial derivative identically zero is of the form (*). There is a function with generalized symmetric mixed partial derivative identically zero not of the form (*), but (*) does follow here with the additional assumpt...

We consider a 2D stochastic wave equation driven by Gaussian noise, which is temporally white and spatially colored described the Riesz kernel. Our first main result functional central limit theorem for spatial average of solution. And we also establish quantitative marginal rate convergence total-variation distance. A fundamental ingredient in our proofs pointwise Lp-estimate Malliavin derivat...