Related papers: Inverse Scattering Problem for Vector Fields and t…
We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which…
We study the Cauchy problem for the one-dimensional wave equation with an inverse square potential. We derive dispersive estimates, energy estimates, and estimates involving the scaling vector field, where the latter are obtained by…
In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.
An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions…
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…
Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation…
In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave…
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.
Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
We have recently solved the inverse spectral problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…
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…
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 pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
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.…