Related papers: The cubic NLS on the line with an inverse square p…
We prove that solutions to non-linear Schr\"odinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non-linear potential is defocusing and grows at least as the…
We study the inverse problem of determining a time-dependent globally hyperbolic Lorentzian metric from the scattering operator for semilinear wave equations.
We solve inverse scattering problem for Schr\"odinger operators with compactly supported potentials on the half line. We discretize S-matrix: we take the value of the S-matrix on some infinite sequence of positive real numbers. Using this…
We consider the asymptotics of the one-dimensional cubic nonlinear Schr\"odinger equation with an external potential $V$ that does not admit bound states. Assuming that $\jBra{x}^{2+}V(x) \in L^1$ and that $u$ is orthogonal to any…
A condition, at which the one-dimensional inverse power potential becomes reflectionless during propagation through it of a plane wave, is obtained on the basis of SUSY QM methods. A scattering of a particle on spherically symmetric inverse…
The present status of the coupled-channel inverse-scattering method with supersymmetric transformations is reviewed. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a…
In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral…
In this work we consider the wave equation with a repulsive potential, either on the half line ${\mathbb R}^+$ or the Euclidean space ${\mathbb R}^d$ with $d\geq 3$. We combine the operator theory and the inward/outward energy theory to…
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…
In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…
We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set…
The local and non-local vector Non-linear Schrodinger Equation (NLSE) with a general cubic non-linearity are considered in presence of a linear term characterized, in general, by a non-hermitian matrix which under certain condition…
We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schr\" odinger equation (NLS) with an attractive localized potential and a time-dependent factor in the nonlinearity. We show that, under generic hypotheses on…
The aims of the reported work are to provide new insights into the quantum dot optical properties confined in an inverse of a quadratic Hellmann potential. The Schr\"odinger equation is solved using the Nikiforov-Uvarov (NU) method, in…
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of…
This article is concerned with the small data problem for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global…
The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in terms of the structure and in terms of the spectral features of…
We prove $H^{1}$ scattering for a defocusing NLS on the line with fully variable coefficients. The result is proved by adapting the Kenig--Merle scheme to a non translation invariant setting. In addition, we give an abstract version of the…