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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02434 |
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| _version_ | 1866913223032176640 |
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| author | Bessonov, R. V. Gubkin, P. V. |
| author_facet | Bessonov, R. V. Gubkin, P. V. |
| contents | We prove a sharp stability estimate for Schur iterates of contractive analytic functions in the open unit disk. We then apply this result in the setting of the inverse scattering approach and obtain a fast algorithm for solving the discrete integrable nonlinear Schrödinger equation (Ablowitz-Ladik equation) on the integer lattice, $\mathbb{Z}$. We also give a self-contained introduction to the theory of the nonlinear Fourier transform from the perspective of Schur functions and orthogonal polynomials on the unit circle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Schur's iterates and fast solution of the discrete integrable NLS Bessonov, R. V. Gubkin, P. V. Spectral Theory We prove a sharp stability estimate for Schur iterates of contractive analytic functions in the open unit disk. We then apply this result in the setting of the inverse scattering approach and obtain a fast algorithm for solving the discrete integrable nonlinear Schrödinger equation (Ablowitz-Ladik equation) on the integer lattice, $\mathbb{Z}$. We also give a self-contained introduction to the theory of the nonlinear Fourier transform from the perspective of Schur functions and orthogonal polynomials on the unit circle. |
| title | Stability of Schur's iterates and fast solution of the discrete integrable NLS |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2402.02434 |