Related papers: A note on the partial data inverse problem for a n…
The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a…
We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schr\"odinger operator on the half line. The goal of the paper is to establish the connections between different types of inverse data for these…
In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient $\beta(t, x)$ in the Schr\"odinger equation $(i\partial_t + \Delta + q(t, x))u + \beta u^2 = 0$, from the boundary…
This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the…
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…
We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for…
We consider magnetic Schr\"odinger equations with sublinear magnetic potentials and subquadratic electric potentials on $\mathbb{R}^{d}$, as well as generalizations thereof. We obtain new results on the global well-posedness of the Cauchy…
We prove analyticity of solutions in $\mathbb{R}^{n}$, $n\ge1$, to certain nonlocal linear Schr\"odinger equations with analytic potentials.
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schr\"odinger operator with a periodic potential plus a finitely supported perturbation. We describe all…
We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…
We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…
In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…
This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…
The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the…
We study the inverse problem of determining the magnetic field and the electric potential entering the Schr\"odinger equation in an infinite 3D cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we consider is a closed…
A particular instance of the inverse magnetisation problem is considered. It is assumed that the support of a magnetic sample (a source term in the Poisson equation in $\mathbb{R}^3$) is contained in a bounded planar set parallel to the…
We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances…
We prove a reverse Lieb-Thirring inequality with a sharp constant for the matrix Schr\"odinger equation on the half-line.
We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schr\"odinger equation in a bounded domain of $\mathbb R^n$, $n\geq 2$, by boundary observation of the solution over the entire…
We consider a magnetic Schr\"odinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the…