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We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation $u_{xt}=u+\frac{1}{6}(u^3)_{xx}$ with zero boundary conditions (as $|x|\to\infty$). This approach is directly applied to the…

Exactly Solvable and Integrable Systems · Physics 2016-09-07 Anne Boutet de Monvel , Dmitry Shepelsky , Lech Zielinski

We study an inverse scattering problem for a pair of Hamiltonians $(H(h), H\_0 (h))$ on $L^2 (\r^n)$, where $H\_0 (h) = -h^2 \Delta$ and $H (h)= H\_0 (h) +V$, $V$ is a short-range potential with a regular behaviour at infinity and $h$ is…

Mathematical Physics · Physics 2007-05-23 François Nicoleau

The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…

Mathematical Physics · Physics 2020-05-22 Tuncay Aktosun , Ricardo Weder

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

Mathematical Physics · Physics 2011-11-10 Ole Henrik Waagaard , Johannes Skaar

This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…

Analysis of PDEs · Mathematics 2020-08-26 Sophia Bugarija , Peter C. Gibson , Guanghui Hu , Peijun Li , Yue Zhao

Scattering of refracting Huygens' metasurfaces is revisited. A new analytical closed-form solution is obtained for the two-dimensional problem under transverse electric (TE) plane-wave incidence -- a solution which gives the scattering for…

Classical Physics · Physics 2022-11-08 Gleb A. Egorov , George V. Eleftheriades

In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the tcCH equations with $4\times4$ the Lax pair.…

Exactly Solvable and Integrable Systems · Physics 2019-11-11 Xin Wu , Shou-Fu Tian , Jin-Jie Yang

This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…

Spectral Theory · Mathematics 2023-03-24 Natalia P. Bondarenko

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…

Mathematical Physics · Physics 2020-10-08 Evgeny L. Korotyaev

We revisit the total scatterings (in terms of extinction, scattering and absorption cross sections) by arbitrary clusters of nonmagnetic particles that support optically-induced magnetic responses. Our reexamination is conducted from the…

Optics · Physics 2020-09-23 Qingdong Yang , Weijin Chen , Yuntian Chen , Wei Liu

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Marlena Nowaczyk , Bruce Alastair Watson

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.

Mathematical Physics · Physics 2017-08-29 Xiao-Chuan Xu , Chuan-Fu Yang

This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…

Analysis of PDEs · Mathematics 2023-12-08 Heping Dong , Peijun Li

A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…

Mathematical Physics · Physics 2007-05-23 Tuncay Aktosun , Vassilis G. Papanicolaou , Vassilis Zisis

We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…

Analysis of PDEs · Mathematics 2020-01-29 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…

Analysis of PDEs · Mathematics 2012-06-27 A. G. Ramm

We investigate the scattering problem of a two-particle composite system on a delta-function potential. Using the time independent scattering theory, we study how the transmission/reflection coefficients change with the height of external…

Quantum Physics · Physics 2017-01-26 Tieling Song , Wei Zhu , D. L. Zhou

We investigate the Manakov model or, more generally, the vector nonlinear Schr\"odinger equation on the half-line. Using a B\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet…

Mathematical Physics · Physics 2015-05-30 V. Caudrelier , Q. C. Zhang

In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…

Exactly Solvable and Integrable Systems · Physics 2020-04-03 Zhou-Zheng Kang , Tie-Cheng Xia
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