Related papers: Dispersion for the wave and Schr\"odinger equation…
We show global asymptotic stability of solitary waves of the nonlinear Schr\"odinger equation in space dimension 1. Furthermore, the radiation is shown to exhibit long range scattering if the nonlinearity is cubic at the origin, or standard…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
We prove a dispersive estimate for the one-dimensional Schroedinger equation, mapping between weighted $L^p$ spaces with stronger time-decay ($t^{-3/2}$ versus $t^{-1/2}$) than is possible on unweighted spaces. To satisfy this bound, the…
This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data,…
We establish dispersive and Strichartz estimates for solutions to the linear time-dependent Schr\"odinger equations with potential in three dimensions. Our main focus is on the small rough time-dependent potentials. Examples of such…
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…
We deal with the wave equation with assigned moving boundary ($0<x<a(t)$) upon which Dirichlet or mixed boundary conditions are specified, here $a(t)$ is assumed to move slower than the light and periodically. Moreover $a$ is continuous,…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
The main objective of this paper is understanding the propagation laws obeyed by high-frequency limits of Wigner distributions associated to solutions to the Schroedinger equation on the standard d-dimensional torus T^{d}. From the point of…
We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $\Omega\subset\mathbb{R}^N$ ($N\geq 2$). {In a subregion $D\Subset\Omega$, the medium is supposed to be lossy and have a large…
In this paper, we study boundary-value problems describing the exit distribution of finite-velocity random motions from prescribed domains. For the standard telegraph process, with and without drift, we derive the Dirichlet problems…
We study the Dirichlet problem for the non-local diffusion equation $u_t=\int\{u(x+z,t)-u(x,t)\}\dmu(z)$, where $\mu$ is a $L^1$ function and $``u=\phi$ on $\partial\Omega\times(0,\infty)$'' has to be understood in a non-classical sense. We…
We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. \"Osterreich. Akad. Wiss.…
We consider the defocusing energy-critical NLS in the exterior of the unit ball in three dimensions. For the initial value problem with Dirichlet boundary condition we prove global well-posedness and scattering with large radial initial…
We analyze the refocusing properties of time reversed waves that propagate in two different media during the forward and backward stages of a time-reversal experiment. We consider two regimes of wave propagation modeled by the paraxial wave…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…