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

Standard

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations. / Frumin, Leonid L.

In: Journal of Inverse and Ill-Posed Problems, Vol. 29, No. 3, 01.06.2021, p. 369-383.

Research output: Contribution to journal › Article › peer-review

Harvard

Frumin, LL 2021, 'Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations', Journal of Inverse and Ill-Posed Problems, vol. 29, no. 3, pp. 369-383. https://doi.org/10.1515/jiip-2020-0126

APA

Frumin, L. L. (2021). Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations. Journal of Inverse and Ill-Posed Problems, 29(3), 369-383. https://doi.org/10.1515/jiip-2020-0126

Vancouver

Frumin LL. Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations. Journal of Inverse and Ill-Posed Problems. 2021 Jun 1;29(3):369-383. Epub 2020 Dec 2. doi: 10.1515/jiip-2020-0126

Author

Frumin, Leonid L. / Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations. In: Journal of Inverse and Ill-Posed Problems. 2021 ; Vol. 29, No. 3. pp. 369-383.

BibTeX

@article{736ae2754e2546a08c503c9c43173c57,

title = "Algorithms for solving scattering problems for the Manakov model of nonlinear Schr{\"o}dinger equations",

abstract = "We introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schr{\"o}dinger 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.",

keywords = "algorithm, inverse, Nonlinear, polarization, scattering, soliton",

author = "Frumin, {Leonid L.}",

year = "2021",

month = jun,

day = "1",

doi = "10.1515/jiip-2020-0126",

language = "English",

volume = "29",

pages = "369--383",

journal = "Journal of Inverse and Ill-Posed Problems",

issn = "0928-0219",

publisher = "Walter de Gruyter GmbH",

number = "3",

}

RIS

TY - JOUR

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

AU - Frumin, Leonid L.

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 -

ID: 28466767