Related papers: Time-dependent methods in inverse scattering probl…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…
Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…
The use of leading order effective field theory (EFT) to describe neutron-deuteron scattering leads to integral equations that have unusual behaviour: when only two-body interactions are included, the scattering amplitude does not approach…
Strong interactions produce a rich spectrum of resonances that decay into three or more hadrons. Understanding their phenomenology requires a theoretical framework to extract parameters fromexperimental data and Lattice QCD simulations of…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
Inverting scattering experiments to obtain effective interparticle interactions is generally a poorly conditioned problem. L. Reatto (Phil. Mag. A 58, 37 (1986)) showed that for atomic liquids close to the triple point, inversions are hard…
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 inverse-scattering problem of an inhomogeneous material has been of interest for many years, and was generally addressed with various optimization techniques. In this paper, we suggest an optimization-free method for solving the…
The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which…
\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
We study a generalized defocusing Hartree equation with nonlocal exchange potential and repulsive Hartree--Fock interaction. Using an inverse optimal problem (IOP) approach, we prove the existence and uniqueness of ground state solutions.…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
A generalized inverse scattering method has been applied to the linear problem associated with the coupled higher order nonlinear schr\"odinger equation to obtain it's $N$-soliton solution. An infinite number of conserved quantities have…