TY - JOUR

T1 - Block Toeplitz Inner-Bordering method for the Gelfand-Levitan-Marchenko equations associated with the Zakharov-Shabat system

AU - Medvedev, Sergey

AU - Vaseva, Irina

AU - Fedoruk, Mikhail

N1 - The work of S. Medvedev and M. Fedoruk (analytical results) is supported by a grant of the Russian Science Foundation (Project No. 22-11-00287, https://rscf.ru/en/project/22-11-00287/) carried out in the Federal Research Center for Information and Computational Technologies. The work of I. Vaseva (numerical results) is supported by the state funding program FSUS-2020-0034.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - We propose a generalized method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB). The method works for the signals containing both the continuous and the discrete spectra. The method allows us to calculate the potential at an arbitrary point and does not require small spectral data. Using this property, we can perform calculations to the right and to the left of the selected starting point. For the discrete spectrum, the procedure of cutting off exponentially growing matrix elements is suggested to avoid the numerical instability and perform calculations for soliton solutions spaced apart in the time domain.

AB - We propose a generalized method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB). The method works for the signals containing both the continuous and the discrete spectra. The method allows us to calculate the potential at an arbitrary point and does not require small spectral data. Using this property, we can perform calculations to the right and to the left of the selected starting point. For the discrete spectrum, the procedure of cutting off exponentially growing matrix elements is suggested to avoid the numerical instability and perform calculations for soliton solutions spaced apart in the time domain.

KW - Gelfand-Levitan-Marchenko equation

KW - Toeplitz Inner-Bordering method

KW - inverse scattering transform

KW - nonlinear Fourier transform

KW - nonlinear Schrodinger equation

UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85147896144&partnerID=40&md5=d7dbacc3238518b49cd48a567b47680d

UR - https://www.mendeley.com/catalogue/db755eb4-337d-3771-83e3-4904f610b36e/

U2 - 10.1515/jiip-2022-0072

DO - 10.1515/jiip-2022-0072

M3 - Article

VL - 31

SP - 191

EP - 202

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 2

ER -