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

  • Roman Bessonov

    St. Petersburg State University, St. Petersburg, Russia; St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia
  • Pavel Gubkin

    St. Petersburg State University, St. Petersburg, Russia; St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia
Stability of Schur’s iterates and fast solution of the discrete integrable NLS cover
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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 Schrödinger equation (Ablowitz–Ladik equation) on the integer lattice, . 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.

Cite this article

Roman Bessonov, Pavel Gubkin, Stability of Schur’s iterates and fast solution of the discrete integrable NLS. J. Spectr. Theory 15 (2025), no. 1, pp. 149–194

DOI 10.4171/JST/537