Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013078 |
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| _version_ | 1832592139733696512 |
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| author | David B. Reinhardt Dean Lee Wolfgang P. Schleich Matthias Meister |
| author_facet | David B. Reinhardt Dean Lee Wolfgang P. Schleich Matthias Meister |
| author_sort | David B. Reinhardt |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-45fef7ebc6a74665be1f627aa01b9634 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-45fef7ebc6a74665be1f627aa01b96342025-01-21T15:02:52ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101307810.1103/PhysRevResearch.7.013078Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimationDavid B. ReinhardtDean LeeWolfgang P. SchleichMatthias MeisterThe 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.http://doi.org/10.1103/PhysRevResearch.7.013078 |
| spellingShingle | David B. Reinhardt Dean Lee Wolfgang P. Schleich Matthias Meister Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation Physical Review Research |
| title | Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation |
| title_full | Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation |
| title_fullStr | Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation |
| title_full_unstemmed | Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation |
| title_short | Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation |
| title_sort | conformal duality of the nonlinear schrodinger equation theory and applications to parameter estimation |
| url | http://doi.org/10.1103/PhysRevResearch.7.013078 |
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