TY - JOUR

T1 - Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

AU - Frumin, Leonid L.

N1 - Publisher Copyright: © 2020 Walter de Gruyter GmbH, Berlin/Boston. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem's efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand-Levitan-Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson's type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms' efficiency and stability. We also present an example of the algorithms' application to simulate the Manakov vector solitons' collision.

AB - We introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem's efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand-Levitan-Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson's type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms' efficiency and stability. We also present an example of the algorithms' application to simulate the Manakov vector solitons' collision.

KW - algorithm

KW - inverse

KW - Nonlinear

KW - polarization

KW - scattering

KW - soliton

UR - http://www.scopus.com/inward/record.url?scp=85097490828&partnerID=8YFLogxK

U2 - 10.1515/jiip-2020-0126

DO - 10.1515/jiip-2020-0126

M3 - Article

AN - SCOPUS:85097490828

VL - 29

SP - 369

EP - 383

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 3

ER -