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A new method for directly sampling the neutron resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches,…

Computational Physics · Physics 2023-03-16 Gavin Ridley , Benoit Forget , Timothy Burke

The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…

Information Theory · Computer Science 2015-11-24 Sander Wahls , H. Vincent Poor

The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…

Numerical Analysis · Mathematics 2018-01-09 Xiaodong Liu , Jiguang Sun

We propose an inverse scattering transform for the continuum Calogero-Moser equation. We give a rigorous treatment of the direct scattering problem by constructing the associated Jost solutions and introducing a distorted Fourier transform,…

Analysis of PDEs · Mathematics 2025-10-14 Rupert L. Frank , Larry Read

We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical…

Quantum Physics · Physics 2010-05-25 W. B. Cardoso , A. T. Avelar , D. Bazeia

In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schr\"{o}dinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with $t=0$ are…

Exactly Solvable and Integrable Systems · Physics 2020-05-05 Xin Wu , Shou-Fu Tian , Jin-Jie Yang

Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity…

Numerical Analysis · Mathematics 2020-04-24 Xiaokai Yuan , Gang Bao , Peijun Li

We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the…

Pattern Formation and Solitons · Physics 2009-11-11 J. Gomez-Gardenes , L. M. Floria , A. R. Bishop

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…

Numerical Analysis · Mathematics 2018-05-01 Xiaoli Liu , Bo Zhang , Haiwen Zhang

We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…

Mathematical Physics · Physics 2023-10-03 Farhang Loran , Ali Mostafazadeh

Relying upon tools from the theory of integrable systems, we discuss the linear instability of the Kuznetsov-Ma breathers and the Akhmediev breathers of the focusing nonlinear Schr{\"o}dinger equation. We use the Darboux transformation to…

Analysis of PDEs · Mathematics 2021-12-30 Mariana Haragus , Dmitry Pelinovsky

This paper concerns the numerical simulation of time domain inverse acoustic scattering problems with a point-like scatterer, multiple point-like scatterers or normal size scatterers. Based on the Green's function and the application of the…

Numerical Analysis · Mathematics 2024-06-07 Qingqing Yu , Bo Chen , Jiaru Wang , Yao Sun

In this article, the inverse scattering transform is considered for the Gerdjikov-Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann-Hilbert (RH) method. The formula of the soliton solutions are established by…

Exactly Solvable and Integrable Systems · Physics 2020-12-29 Zhang Zechuan , Fan Engui

The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring…

Nuclear Theory · Physics 2009-11-06 V. S. Vasilevsky , F. Arickx

Practical applications of microwave imaging often require the solution of inverse scattering problems with inhomogeneous backgrounds. Towards this end, a novel inversion strategy, which combines the multi-scaling (MS) regularization scheme…

Signal Processing · Electrical Eng. & Systems 2024-01-08 Yu Zhong , Francesco Zardi , Marco Salucci , Giacomo Oliveri , Andrea Massa

We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then…

Mathematical Physics · Physics 2015-06-02 Vincent Caudrelier

We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity…

Pattern Formation and Solitons · Physics 2022-09-20 Alexander Hrabski , Yulin Pan

Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain the square k^2 of a focusing modified Korteweg-de Vries (mKdV) breather solution with non zero vacuum parameter b^2 . We are able to factorize and…

Mathematical Physics · Physics 2011-10-19 Miguel A. Alejo

Study of scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of…

Nuclear Theory · Physics 2018-08-09 N. J. Upadhyay , A. Bhagwat

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we…

Analysis of PDEs · Mathematics 2023-05-25 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld