Related papers: Wave packet analysis of Schrodinger equations in a…
The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for the numerical simulation of semiclassical wave propagation,…
We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in…
In this article we prove time-global smoothing effects of dispersive pseudodifferential equations with constant coefficient radially symmetric symbols on real rank one symmetric spaces of noncompact type. We also discuss gain of…
We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of…
Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…
We show that the exact discrete analogue of Schr\"odinger equation can be derived naturally from the Hamiltonian operator of a Schr\"odinger field theory by using the discrete Fourier transform that transforms the operator from momentum…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
Under investigation in this work is an extended nonlinear Schr\"{o}dinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation…
We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators…
We build Gaussian wave packets for the linear Schr\"odinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua,…
We prove global weighted Strichartz estimates for radial solutions of linear Schr\"odinger equation on a class of rotationally symmetric noncompact manifolds, generalizing the known results on hyperbolic and Damek-Ricci spaces. This yields…
We argue that the way to get the general solution of a Schrodinger equation in the presence of a time-dependent linear potential based on the Lewis-Riesenfeld framework is to use a Hermitian linear invariant operator. We demonstrate that…
The present paper is devoted to the semiclassical analysis of linear Schr\"odinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order…
We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schr\"{o}dinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial…
The present paper is dedicated to the proof of dispersive estimates on stratified Lie groups of step 2, for the linear Schr\"odinger equation involving a sublaplacian. It turns out that the propagator behaves like a wave operator on a space…
We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile…
In this paper we study the asymptotic behavior of a quadratic Schr\"{o}dinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non…