Symmetries of the Hirota Difference Equation
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of the...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148569 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Symmetries of the Hirota Difference Equation / A.K. Pogrebkov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653942711713792 |
|---|---|
| author | Pogrebkov, A.K. |
| author_facet | Pogrebkov, A.K. |
| citation_txt | Symmetries of the Hirota Difference Equation / A.K. Pogrebkov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as ''times'' of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented.
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| first_indexed | 2025-12-01T23:49:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148569 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:49:48Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Pogrebkov, A.K. 2019-02-18T15:59:00Z 2019-02-18T15:59:00Z 2017 Symmetries of the Hirota Difference Equation / A.K. Pogrebkov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q51; 37K10; 37K15; 37K40; 39A14 DOI:10.3842/SIGMA.2017.053 https://nasplib.isofts.kiev.ua/handle/123456789/148569 Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as ''times'' of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented. This work has been funded by the Russian Academic Excellence Project ‘5-100’. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries of the Hirota Difference Equation Article published earlier |
| spellingShingle | Symmetries of the Hirota Difference Equation Pogrebkov, A.K. |
| title | Symmetries of the Hirota Difference Equation |
| title_full | Symmetries of the Hirota Difference Equation |
| title_fullStr | Symmetries of the Hirota Difference Equation |
| title_full_unstemmed | Symmetries of the Hirota Difference Equation |
| title_short | Symmetries of the Hirota Difference Equation |
| title_sort | symmetries of the hirota difference equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148569 |
| work_keys_str_mv | AT pogrebkovak symmetriesofthehirotadifferenceequation |