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The L\"uscher scattering formalism, the standard approach for relating the discrete finite-volume energy spectrum to two-to-two scattering amplitudes, fails when analytically continued so far below the infinite-volume two-particle threshold…
We study the scattering of a massless scalar field in a generic Kerr background. Using a particular gauge choice based on the current conservation of the radial equation, we give a generic formula for the scattering coefficient in terms of…
We derive a linear model of navigation in a two-layer fluid with a variable velocity of the ship. A spectral version of the model including a Rayleigh damping term is analyzed. We prove that the Cauchy problem has a unique solution if the…
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…
We consider the Cauchy problem for a family of semilinear defocusing Schr\"odinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle…
The problems we address in this paper are the spectral theory and the inverse problems associated with Laplacians on non-compact Riemannian manifolds and more general manifolds admitting conic singularities. In particular, we study the…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
In this paper, we study the scattering for the nonlinear beam equation $u_{tt}+\Delta^2u+mu+\mu |u|^{p-1}u=0$. Our results include two aspects. In the defocusing case we show that the scattering holds for $d=1$, which extends the result in…
Exploring the interaction of light with time-varying media is an intellectual challenge that, in addition to fundamental aspects, provides a pathway to multiple promising applications. Time modulation constitutes here a fundamental handle…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the…
The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more-cylindrical cavity systems, and compared to an elastodynamic generalization of the semi-classical Gutzwiller unstable periodic…
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…
The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse…
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here…
Using numerical simulations, the stability and scattering properties of the O(3) model on a two-dimensional torus are studied. Its solitons are found to be unstable but can be stabilized by the addition of a Skyrme term to the Lagrangian.…