Related papers: Scattering and inverse scattering for multipoint p…
We consider the scattering transform for the Schr\"odinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of…
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…
A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent…
Starting from the semi-classical spectrum of Schr\"odinger operators $-h^2\Delta+V$ (on $\mathbb{R}^n$ or on a Riemannian manifold) it is possible to detect critical levels of the potential $V$. Via micro-local methods one can express…
We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…
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,…
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…
We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…
We solve inverse scattering problem for Schr\"odinger operators with compactly supported potentials on the half line. We discretize S-matrix: we take the value of the S-matrix on some infinite sequence of positive real numbers. Using this…
In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schr\"{o}dinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some…
The scattering problem under the influence of the Aharonov-Bohm (AB) potential is reconsidered. By solving the Lippmann-Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a…
We define scattering data for the relativistic Newton equation in an electric field $-\nabla V\in C^1(\R^n,\R^n)$, $n\ge 2$, and in a magnetic field $B\in C^1(\R^n,A_n(\R))$ that decay at infinity like $r^{-\alpha-1}$ for some $\alpha\in…
Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as…
We consider a class of nonlinear Schr\"odinger equations with potential \[ i\partial_t u +\Delta u - Vu = \pm |u|^\alpha u, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3, \] where $\frac{4}{3}<\alpha<4$ and $V$ is a Kato-type potential. We…
We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…