Scattering data computation for the Zakharov-Shabat system
Luisa Fermo, Cornelis van der Mee, Sebastiano Seatzu
TL;DR
This paper introduces a numerical method for solving the direct scattering problem of the Zakharov-Shabat system, crucial for analyzing the nonlinear Schrödinger equation, using integral equations and exponential sum identification.
Contribution
It presents a novel numerical approach combining Volterra integral solutions and parameter identification for the Zakharov-Shabat system.
Findings
Numerical experiments demonstrate the method's effectiveness.
The approach accurately computes scattering data.
The technique is efficient for the inverse scattering transform.
Abstract
A numerical method to solve the direct scattering problem for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schroedinger equation is proposed. The method involves the numerical solution of Volterra integral systems with structured kernels and the identification of coefficients and parameters appearing in monomial-exponential sums. Numerical experiments confirm the effectiveness of the proposed technique.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Advanced Mathematical Physics Problems