Related papers: Construction of modified wave operators via wave p…
In this paper, we give a characterization of the ranges of the wave operators for Schrodinger equations with time-dependent short-range potentials by using wave packet transform. We also give an alternative proof of the existence of the…
We construct time-dependent wave operators for Schr\"{o}dinger equations with long-range potentials on a manifold $M$ with asymptotically conic structure. We use the two space scattering theory formalism, and a reference operator on a space…
We consider the scattering theory for discrete Schr\"odinger operators on $Z^d$ with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
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 prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
In this paper, we define time-independent modifiers to construct a long-range scattering theory for discrete schr\"odinger operators on the square lattice $\mathbb{Z}^N$. We prove the existence and completeness of modified wave operators in…
In the present paper, we construct modified wave operators for the defocusing cubic nonlinear Schr\"odinger equation (NLS) in one space dimension without size restriction on scattering data. In the proof, we introduce a new formulation of…
We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave…
We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schr\"odinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator…
In this article, we determine the wave front sets of solutions to time dependent Schr\"odinger equations with a sub-quadratic potential by using the representation of the Schr\"dingier evolution operator via wave packet transform (short…
We obtain structure formulas for the intertwining wave operators of a Schroedinger operator with potential V in R^3. The difference from our previous submission arXiv:1612.07304 lies with the fact that here we impose a scaling invariant…
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular the existence of modified wave operators for that system with…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…
The solution of the Schrodinger equation with a linear potential is considered. We use algebraic methods to obtain the explicit form of the solution for the explicitly time dependent Hamiltonian and discuss the general conditions which…
In this article we give explicit solutions for the wave equations associated to the modified Schr\"odinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified…
We consider the final state problem for the inhomogeneous nonlinear Schr\"odinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a logarithmic phase correction compared with the free…
In this note we give an explicit formula for the wave equation associated to the Schrodinger operator with a Liouville Potential with applications to the telegraph equation as well as the wave equation on the hyperbolic plane
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…