The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System
We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An auto-Bäcklund transformation and a superposition formula for the NLS-type...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211419 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System. Dmitry K. Demskoi. SIGMA 17 (2021), 108, 10 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862687454920704000 |
|---|---|
| author | Demskoi, Dmitry K. |
| author_facet | Demskoi, Dmitry K. |
| citation_txt | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System. Dmitry K. Demskoi. SIGMA 17 (2021), 108, 10 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An auto-Bäcklund transformation and a superposition formula for the NLS-type system are obtained by elimination of shifts from the lattice sine-Gordon equation and its down-shifted version. We use the obtained formulae to calculate a superposition of two and three elementary solutions.
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| first_indexed | 2026-03-17T13:52:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211419 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T13:52:13Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Demskoi, Dmitry K. 2026-01-02T08:28:51Z 2021 The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System. Dmitry K. Demskoi. SIGMA 17 (2021), 108, 10 pages 1815-0659 2020 Mathematics Subject Classification: 35Q51; 35Q55; 37K60 arXiv:2101.04332 https://nasplib.isofts.kiev.ua/handle/123456789/211419 https://doi.org/10.3842/SIGMA.2021.108 We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An auto-Bäcklund transformation and a superposition formula for the NLS-type system are obtained by elimination of shifts from the lattice sine-Gordon equation and its down-shifted version. We use the obtained formulae to calculate a superposition of two and three elementary solutions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System Article published earlier |
| spellingShingle | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System Demskoi, Dmitry K. |
| title | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System |
| title_full | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System |
| title_fullStr | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System |
| title_full_unstemmed | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System |
| title_short | The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System |
| title_sort | lattice sine-gordon equation as a superposition formula for an nls-type system |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211419 |
| work_keys_str_mv | AT demskoidmitryk thelatticesinegordonequationasasuperpositionformulaforannlstypesystem AT demskoidmitryk latticesinegordonequationasasuperpositionformulaforannlstypesystem |