Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation

Reinhardt, David B.; Lee, Dean; Schleich, Wolfgang P.; Meister, Matthias

doi:10.1103/PhysRevResearch.7.013078

Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation

Journal Article · Tue Jan 21 00:00:00 EST 2025 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.7.013078· OSTI ID:2504230

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The nonlinear Schrödinger equation (NLSE) in one spatial dimension has stationary solutions similar to those of the linear Schrödinger equation (LSE) as well as more exotic solutions such as solitary waves and quantum droplets. Here, we present a newly discovered conformal duality which unifies the stationary and time-dependent traveling-wave solutions of the one-dimensional cubic-quintic NLSE, the cubic NLSE and LSE. Any two systems that are classified by the same single number called the cross ratio are related by this symmetry. Notably, the conformal duality can also be adapted in Newtonian mechanics and serves as a powerful tool for investigating physical systems that otherwise cannot be directly accessed in experiments. Further, we show that the conformal symmetry is a valuable resource to substantially improve NLSE parameter estimation from noisy empirical data by introducing an optimization afterburner. The new method therefore has far reaching practical applications for nonlinear physical systems.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0013365; SC0021152; SC0023658

OSTI ID:: 2504230

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 1 Vol. 7; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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