Abstract
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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 22-11-00287
Award Identifier / Grant number: FSUS-2020-0034
Funding statement: 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.
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