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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2006
Hauptverfasser: He, Jingsong, Li, Yinghua, Cheng, Yi
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2006
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146112
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146112
record_format dspace
spelling He, Jingsong
Li, Yinghua
Cheng, Yi
2019-02-07T13:43:38Z
2019-02-07T13:43:38Z
2006
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
https://nasplib.isofts.kiev.ua/handle/123456789/146112
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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
spellingShingle q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
He, Jingsong
Li, Yinghua
Cheng, Yi
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
author He, Jingsong
Li, Yinghua
Cheng, Yi
author_facet He, Jingsong
Li, Yinghua
Cheng, Yi
publishDate 2006
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146112
fulltext
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.
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AT chengyi qdeformedkphierarchyandqdeformedconstrainedkphierarchy
first_indexed 2025-11-24T06:30:06Z
last_indexed 2025-11-24T06:30:06Z
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