Stability of Schur's iterates and fast solution of the discrete integrable NLS

R. V. Bessonov; P. V. Gubkin

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arXiv · 2402.02434

Stability of Schur's iterates and fast solution of the discrete integrable NLS

R. V. Bessonov·P. V. Gubkin

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Abstract

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 Schr\"odinger 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.

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BibTeX RIS

R. V. Bessonov, P. V. Gubkin. 2024-02-04. Stability of Schur's iterates and fast solution of the discrete integrable NLS. https://arxiv.org/abs/2402.02434

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