Moving Frames: Difference and Differential-Difference Lagrangians
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising fr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212117 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Moving Frames: Difference and Differential-Difference Lagrangians. Lewis C. White and Peter E. Hydon. SIGMA 20 (2024), 006, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735217392877568 |
|---|---|
| author | White, Lewis C. Hydon, Peter E. |
| author_facet | White, Lewis C. Hydon, Peter E. |
| citation_txt | Moving Frames: Difference and Differential-Difference Lagrangians. Lewis C. White and Peter E. Hydon. SIGMA 20 (2024), 006, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the nonlinear Schrödinger equation.
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| first_indexed | 2026-04-17T16:18:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212117 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:18:55Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | White, Lewis C. Hydon, Peter E. 2026-01-28T13:57:59Z 2024 Moving Frames: Difference and Differential-Difference Lagrangians. Lewis C. White and Peter E. Hydon. SIGMA 20 (2024), 006, 29 pages 1815-0659 2020 Mathematics Subject Classification: 39A14; 58D19; 47E07 arXiv:2309.09040 https://nasplib.isofts.kiev.ua/handle/123456789/212117 https://doi.org/10.3842/SIGMA.2024.006 This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the equivariant formulation of the conservation laws arising from Noether's theorem. The differential-difference theory is not merely an amalgam of the differential and difference theories, but has additional features that reflect the need for the group action to preserve the prolongation structure. Projectable moving frames are introduced; these cause the invariant derivative operator to commute with shifts in the discrete variables. Examples include a Toda-type equation and a method of lines semi-discretization of the nonlinear Schrödinger equation. We thank Professor Elizabeth Mansfield, whose strong advocacy of moving frames, insight, and encouragement have led to this project. The work was partially supported by EPSRC grant number EP/R513246/1. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Moving Frames: Difference and Differential-Difference Lagrangians Article published earlier |
| spellingShingle | Moving Frames: Difference and Differential-Difference Lagrangians White, Lewis C. Hydon, Peter E. |
| title | Moving Frames: Difference and Differential-Difference Lagrangians |
| title_full | Moving Frames: Difference and Differential-Difference Lagrangians |
| title_fullStr | Moving Frames: Difference and Differential-Difference Lagrangians |
| title_full_unstemmed | Moving Frames: Difference and Differential-Difference Lagrangians |
| title_short | Moving Frames: Difference and Differential-Difference Lagrangians |
| title_sort | moving frames: difference and differential-difference lagrangians |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212117 |
| work_keys_str_mv | AT whitelewisc movingframesdifferenceanddifferentialdifferencelagrangians AT hydonpetere movingframesdifferenceanddifferentialdifferencelagrangians |