Related papers: A New Look at the Multidimensional Inverse Scatter…
We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder in 1995, we prove that the high-velocity limit of the…
On a fixed Riemann surface $(M_0,g_0)$ with $N$ Euclidean ends and genus $g$, we show that, under a topological condition, the scattering matrix $S_V(\la)$ at frequency $\la > 0$ for the operator $\Delta+V$ determines the potential $V$ if…
An inverse scattering problem for a quantized scalar field ${\bm \phi}$ obeying a linear Klein-Gordon equation $(\square + m^2 + V) {\bm \phi} = J \mbox{in $\mathbb{R} \times \mathbb{R}^3$}$ is considered, where $V$ is a repulsive external…
In this paper, we study the linear and nonlinear Schr\"odinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale invariance, and using this property, we demonstrate the…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function,…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
We consider the multidimensional Newton-Einstein equation in static electromagnetic field $$\eqalign{\dot p = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+{1\over c}B(x)\dot x,\cr p={\dot x \over \sqrt{1-{|\dot x|^2 \over c^2}}}, \dot p={dp\over…
We consider the massive Thirring model in the laboratory coordinates and explain how the inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient of our method is to transform the corresponding…
We study an inverse scattering problem at fixed energy for radial magnetic Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge…
We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
Consider the Newton equation in the relativistic case (that is the Newton-Einstein equation) $$\eqalign{\dot p = F(x),& F(x)=-\nabla V(x),\cr p={\dot x \over \sqrt{1-{|\dot x|^2 \over c^2}}},& \dot p={dp\over dt}, \dot x={dx\over dt}, x\in…
We show that fixed energy scattering measurements for the magnetic Schroedinger operator uniquely determine the magnetic field and electric potential in dimensions $n \geq 3$. The magnetic potential, its first derivatives, and the electric…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
We apply inverse scattering theory to calculate the functional derivative of the potential $V(x)$ and wave function $\psi(x,k)$ of a one-dimensional Schr\"odinger operator with respect to the reflection amplitude $r(k)$.
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…
We study the inverse scattering problem for the three dimensional nonlinear Schroedinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of…
We consider the time-dependent Hamiltonian $H(t)= {1 \over 2} p^2 -E(t) \cdot x + V(t,x)$ on $L^2(R^n)$, where the external electric field $E(t)$ and the short-range electric potential $V(t,x)$ are time-periodic with the same period. It is…