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We consider the inhomogeneous fifth-order nonlinear Schr\"{o}dinger (ifoNLS) equation with nonzero boundary condition in detailed. Firstly, the spectral analysis of the scattering problem is carried out. A Riemann surface and affine…

Exactly Solvable and Integrable Systems · Physics 2020-01-24 Jin-Jie Yang , Shou-Fu Tian , Zhi-Qiang Li

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 D. V. Savin , V. V. Sokolov , H. -J. Sommers

In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…

Analysis of PDEs · Mathematics 2026-02-09 Fioralba Cakoni , Michael S. Vogelius

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…

Mesoscale and Nanoscale Physics · Physics 2021-05-10 Kuljit S. Virk

A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of Schr\"odinger particles from non-local separable potentials. Eigenchannel vectors and…

Atomic Physics · Physics 2009-07-28 Remigiusz Augusiak

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is…

Numerical Analysis · Mathematics 2023-12-27 Xiaojuan Liu , Maojun Li , Tao Yin

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

Numerical Analysis · Mathematics 2023-07-31 Oscar P. Bruno , Ambuj Pandey

The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…

Optics · Physics 2020-12-30 Ziwei Zhu , Changxi Zheng

We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution…

Quantum Physics · Physics 2022-04-12 Farhang Loran , Ali Mostafazadeh

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…

Mesoscale and Nanoscale Physics · Physics 2025-04-28 Jared Erb , Nadav Shaibe , Robert Calvo , Daniel Lathrop , Thomas Antonsen , Tsampikos Kottos , Steven M. Anlage

In this article we provide a practical prescription to harness the rigorous microscopic, quantum level descriptions of light-matter systems provided by Hopfield diagonalisation for quantum description of nonlinear scattering. A general…

Mesoscale and Nanoscale Physics · Physics 2017-01-25 Christopher R. Gubbin , Simone De Liberato

In this paper we present a pseudospectral method in the disk. Unlike the methods known until now, the disk is not duplicated. Moreover, we solve the Laplace equation subjected to nonhomogeneous Dirichlet, Neumann and Robin boundary…

Numerical Analysis · Mathematics 2019-04-03 Marcela Molina Meyer , Frank Richard Prieto Medina

We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…

Analysis of PDEs · Mathematics 2019-08-23 Alexander Konschin

The paper aims to apply the inverse scattering transform to the defocusing Hirota equation with fully asymmetric non-zero boundary conditions (NZBCs), addressing scenarios in which the solution's limiting values at spatial infinities…

Exactly Solvable and Integrable Systems · Physics 2024-01-31 Rusuo Ye , Peng-Fei Han , Yi Zhang

We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of…

Quantum Physics · Physics 2019-10-30 Rahul Trivedi , Kevin Fischer , Sattwik Deb Mishra , Jelena Vuckovic

We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization. The convergence is proved using the spectral perturbation theory for compact operators. The…

Numerical Analysis · Mathematics 2018-04-10 Juan Liu , Jiguang Sun , Tiara Turner

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Mathematical Physics · Physics 2010-11-09 Evgeny Lakshtanov , Boris Vainberg

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a…

Numerical Analysis · Mathematics 2016-01-12 Adrianna Gillman

In this work, we extend the Riemann-Hilbert (RH) method in order to study the coupled modified Korteweg-de Vries equation (cmKdV) under nonzero boundary conditions (NZBCs), and successfully find its solutions with their various dynamic…

Exactly Solvable and Integrable Systems · Physics 2021-04-07 Xiao-Fan Zhang , Shou-Fu Tian , Jin-Jie Yang