Work

Infinite-length limit of spectral curves and inverse scattering

Year: 2025

Type: article

Abstract: Integrability equips models of theoretical physics with efficient methods for the exact construction of useful states and their evolution. Relevant tools for classical integrable field models in one spatial dimensional are spectral curves in the case of periodic fields and inverse scattering for asymptotic boundary conditions. Even though the two methods are quite different in many ways, they ought to be related by taking the periodicity length of closed boundary conditions to infinity. Using the Korteweg–de Vries equation and the continuous Heisenberg magnet as prototypical classical integrable field models, we discuss and illustrate how data for spectral curves transforms into asymptotic scattering data. In order to gain intuition and also for concreteness, we review how the elliptic states of these models degenerate into solitons at infinite length.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/adcc6d

Authors: Niklas Beisert, Kunal Gupta

Institutions: ETH Zurich, Institute for Theoretical Physics, Uppsala University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Knut och Alice Wallenbergs Stiftelse, Stiftelsen Olle Engkvist Byggmästare