Related papers: Volkov wave function: its orthonormality and compl…
It is pointed out that the "counter example" presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense…
This article begins with an overview, then gives the precise definition of isotropic turbulence, and follows that with the basic conservation equations, in both real space and wavenumber space. These provide the foundations of all…
A new theory of edge waves over a slowly varying depth.
The physical properties of electromagnetic waves in the presence of a gravitational plane wave are analyzed. Formulas for the Stokes parameters describing the polarization of light are obtained in closed form. The particular case of a…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
The spectra of rogue waves of Manakov equations that exist in both focusing or defocusing regimes are derived in analytic form. These spectra are asymmetric during their whole expansion-contraction cycle. They have triangular shape at each…
I will review the most recent and interesting results from gravitational wave detection experiments, concentrating on recent results from the LIGO Scientific Collaboration (LSC). I will outline the methodologies utilized in the searches,…
I give an overview of the motivations for gravitational-wave research, concentrating on the aspects related to ``fundamental'' physics.
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Due to growing interest in quantum measurement, control and feedback, we reproduce a manuscript from 1992, presenting a simple physical and mathematical derivation of stochastic differential equations for wave functions of probed quantum…
The Ostrovskyi (Ostrovskyi-Vakhnenko/short pulse) equations are ubiquitous models in mathematical physics. They describe water waves under the action of a Coriolis force as well as the amplitude of a "short" pulse in an optical fiber. In…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
The purpose of this note is to give a brief overview on zeta functions of curve singularities and to provide some evidences on how these and global zeta functions associated to singular algebraic curves over perfect fields relate to each…
A widely used stochastic wave equation is the classical wave equation perturbed by a term of It\^o's integral. We show that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the…
The motivation of the note is to obtain a H\"{o}rmander-type $L^2$ estimate for $\bar\partial$ equation. The feature of the new estimate is that the constant is independent of the weight function. Moreover, our estimate can be used for…
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…