相关论文: An evolution equation as the WKB correction in lon…
We consider the cubic Schrodinger equation on the line, for which the scattering theory requires modifications due to long range effects. We revisit the construction of the modified wave operator, and recall the construction of its inverse,…
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 previous papers, we proved the existence of modified wave operators for…
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…
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…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
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…
We consider the cubic nonlinear Schr\"odinger equation with long-range linear potentials in one space dimension, and prove the modified scattering in the energy space for the associated final state problem with a prescribed small asymptotic…
We propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear interactions of localized waves in this setting. This problem…
We study the final state problem for the nonlinear Schr\"{o}dinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic profile which is different from the free evolution, we…
We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3, in the Coulomb gauge. We prove the existence of modified wave operators for that system with no size restriction on the Schr"odinger and Maxwell…
We consider the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leq…
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…
We consider Schr\"odinger operators $H$ on $R^n$ with variable coefficients. Let $H_0=-\frac12\triangle$ be the free Schr\"odinger operator and we suppose $H$ is a "short-range" perturbation of $H_0$. Then, under the nontrapping condition,…
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects…
We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3,in the Coulomb gauge.In the special case of vanishing asymptotic magnetic field,we prove the existence of modified wave operators for that system…
This paper is devoted to the analysis of propagation properties for the solutions of a one-dimensional non-local Schr\"odinger equation involving the fractional Laplace operator $(-d_x^2)^s$, $s\in(0,1)$. We adopt a classical WKB approach…
We study a one-dimensional non-stationary Schr\"odinger equation with a potential slowly depending on time. The corresponding stationary operator depends on time as on a parameter. It has a finite number of negative eigenvalues and…
We consider the semi-classical limit of nonlinear Schrodinger equations in the presence of both a polynomial nonlinearity and thederivative in space of a polynomial nonlinearity. By working in a class of analytic initial data, we do not…
In this paper, we construct a modified wave operators for Schrodinger equations with time-dependent long-range potentials by using wave packet transform and give a proof of the existence of the modified wave operators.
In this paper we consider the long time behavior of solutions to the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times\mathbb{T}^{d}$, $1\leq d\leq4$. For sufficiently small, smooth, decaying data we prove…