Work

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

Year: 2024

Type: article

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, \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.

Source: Journal of Spectral Theory

DOI: 10.4171/jst/537

Authors: Roman Bessonov, Pavel Gubkin

Institutions: St Petersburg University, St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Russian Science Foundation, Ministry of Science and Higher Education of the Russian Federation

Awards: G2258008615, G4473062527, G597338630, G6444257319