Related papers: Inverse scattering method for a soliton cellular a…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional nonlinear $O(3)$ $\sigma$-model is studied using both analytical and numerical methods. General formulae describing fermion…
We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons - radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic…
We consider the spectral theory for discrete Schr\"odinger operators on the hexagonal lattice and their inverse scattering problem. We give a procedure for reconstructing the compactly supported potential from the scattering matrix for all…
Central idea: To obtain the interaction potential using the inverse scattering method, we have employed the Physics-Informed Machine Learning (PIML) approach. In this framework, the machine learning algorithm is guided by the underlying…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
The theory of inverse scattering is developed to study the initial-value problem for the modified matrix Korteweg-de Vries (mmKdV) equation with the $2m\times2m$ $(m\geq 1)$ Lax pairs under the nonzero boundary conditions at infinity. In…
We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate…
We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
The scattering of fermions in the background field of a topological soliton of the modified $(2 + 1)$-dimensional $\mathbb{CP}^{1}$ model is studied here both analytically and numerically. Unlike the original $\mathbb{CP}^{1}$ model, the…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found…
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…
An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
In terms of the crystal base of a quantum affine algebra $U_q(\mathfrak{g})$, we study a soliton cellular automaton (SCA) associated with the exceptional affine Lie algebra $\mathfrak{g}=D_4^{(3)}$. The solitons therein are labeled by the…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…