Related papers: Inverse scattering transform for the focusing two-…

In this paper, we propose a new integrable fractional Fokas--Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the…

We give a brief survey for the recent development of inverse scattering theory on non-compact Riemannian manifolds. The main theme is the reconstruction of the manifold and the metric from the scattering matrix.

Within the framework of the Inverse-Scattering formalism and the Hirota algorithm, soliton solutions of evolution equations are images of {\tau}-functions. Typically, the latter are expressed in terms of exponentials, the arguments of which…

We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence…

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

We combine two-dimensional freeform reflector design with a scattering surface modelled using microfacets, i.e., small specular surfaces representing surface roughness. The model results in a convolution integral for the scattered light…

In this work, inverse scattering transform for the sixth-order nonlinear Schr\"{o}dinger equation with both zero and nonzero boundary conditions at infinity is given, respectively. For the case of zero nonzero boundary conditions, in terms…

This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…

This paper focuses on investigation of the N-coupled Hirota equations arising in an optical fiber. Starting from analyzing the spectral problem, a kind of matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then based on…

We present and study a novel class of one-dimensional Hilbert space eigenfunction transforms that diagonalize analytic difference operators encoding the (reduced) two-particle relativistic hyperbolic Calogero-Moser dynamics. The scattering…

In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…

Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed,…

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…

The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a…

The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…

We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…

This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…