相关论文: Completion problems and scattering problems for Di…

A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…

Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain…

We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a…

In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering…

The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.

We consider the third-order linear differential equation $$\displaystyle\frac{d^3\psi}{dx^3}+Q(x)\,\displaystyle\frac{d\psi}{dx}+P(x)\,\psi=k^3\,\psi,\qquad x\in\mathbb R,$$ where the complex-valued potentials $Q$ and $P$ are assumed to…

The restriction imposed on the J-matrix method of using specific L2 bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range of application of the method to physical problems beyond the…

We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…

Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…

We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a…

A problem of monoenergetic particles pulse reflection from half-infinite stratified medium is considered in conditions of elastic scattering with absorbtion account. The theory is based on multiple scattering series solution of Kolmogorov…

In this work we study the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line. We provide the necessary and sufficient conditions for the solvability of the inverse scattering problem.

The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…

We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…

Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…

A basic problem in linear particle optics is to find a symplectic transformation that brings the (symmetric) beam matrix to a special diagonal form, called normal form. The conventional way to do this involves an eigenvalue-decomposition of…

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

This paper is a continuation of the previous one [Journal xx, xxxxx (2022)]. Here, we reformulate the same J-matrix theory by regularizing the inverse square singular potential. The objective is to restore rapid convergence of the…

Proceeding from optical analogy we propose a new physical interpretation of unitarity saturation leading to antishadowing as a reflective scattering. This interpretation of antishadowing is related to the non-perturbative aspects of strong…

Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…