q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
Using the determinant representation of gauge transformation operator, we have shown that the general form of τ function of the q-KP hierarchy is a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as a special case. On the basis of these, we study the q-deformed constrained...
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146112 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy / Jingsong He, Yinghua Li, Yi Cheng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 40 назв. — англ. |
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irk-123456789-1461122019-02-08T01:23:10Z q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy He, Jingsong Li, Yinghua Cheng, Yi Using the determinant representation of gauge transformation operator, we have shown that the general form of τ function of the q-KP hierarchy is a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as a special case. On the basis of these, we study the q-deformed constrained KP (q-cKP) hierarchy, i.e. l-constraints of q-KP hierarchy. Similar to the ordinary constrained KP (cKP) hierarchy, a large class of solutions of q-cKP hierarchy can be represented by q-deformed Wronskian determinant of functions satisfying a set of linear q-partial differential equations with constant coefficients. We obtained additional conditions for these functions imposed by the constraints. In particular, the effects of q-deformation (q-effects) in single q-soliton from the simplest τ function of the q-KP hierarchy and in multi-q-soliton from one-component q-cKP hierarchy, and their dependence of x and q, were also presented. Finally, we observe that q-soliton tends to the usual soliton of the KP equation when x → 0 and q → 1, simultaneously. 2006 Article q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy / Jingsong He, Yinghua Li, Yi Cheng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 40 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q51; 35Q53; 35Q55 http://dspace.nbuv.gov.ua/handle/123456789/146112 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 |
Using the determinant representation of gauge transformation operator, we have shown that the general form of τ function of the q-KP hierarchy is a q-deformed generalized Wronskian, which includes the q-deformed Wronskian as a special case. On the basis of these, we study the q-deformed constrained KP (q-cKP) hierarchy, i.e. l-constraints of q-KP hierarchy. Similar to the ordinary constrained KP (cKP) hierarchy, a large class of solutions of q-cKP hierarchy can be represented by q-deformed Wronskian determinant of functions satisfying a set of linear q-partial differential equations with constant coefficients. We obtained additional conditions for these functions imposed by the constraints. In particular, the effects of q-deformation (q-effects) in single q-soliton from the simplest τ function of the q-KP hierarchy and in multi-q-soliton from one-component q-cKP hierarchy, and their dependence of x and q, were also presented. Finally, we observe that q-soliton tends to the usual soliton of the KP equation when x → 0 and q → 1, simultaneously. |
| format |
Article |
| author |
He, Jingsong Li, Yinghua Cheng, Yi |
| spellingShingle |
He, Jingsong Li, Yinghua Cheng, Yi q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
He, Jingsong Li, Yinghua Cheng, Yi |
| author_sort |
He, Jingsong |
| title |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy |
| title_short |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy |
| title_full |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy |
| title_fullStr |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy |
| title_full_unstemmed |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy |
| title_sort |
q-deformed kp hierarchy and q-deformed constrained kp hierarchy |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146112 |
| citation_txt |
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy / Jingsong He, Yinghua Li, Yi Cheng // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 40 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:23:51Z |
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2023-05-20T17:23:51Z |
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