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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| Дата: | 2017 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148569 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Symmetries of the Hirota Difference Equation / A.K. Pogrebkov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148569 |
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dspace |
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irk-123456789-1485692019-02-19T01:31:09Z Symmetries of the Hirota Difference Equation Pogrebkov, A.K. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148569 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Pogrebkov, A.K. |
| spellingShingle |
Pogrebkov, A.K. Symmetries of the Hirota Difference Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Pogrebkov, A.K. |
| author_sort |
Pogrebkov, A.K. |
| title |
Symmetries of the Hirota Difference Equation |
| title_short |
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_sort |
symmetries of the hirota difference equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148569 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT pogrebkovak symmetriesofthehirotadifferenceequation |
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2023-05-20T17:30:52Z |
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2023-05-20T17:30:52Z |
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