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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 060, 32 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.060
(Mi sigma88)
 

This article is cited in 44 scientific papers (total in 44 papers)

$q$-Deformed KP Hierarchy and $q$-Deformed Constrained KP Hierarchy

Jingsong Heab, Yinghua Lib, Yi Chengb

a Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
b Department of Mathematics, University of Science and Technology of China, Hefei, 230026 Anhui, P.R. China
References:
Abstract: Using the determinant representation of gauge transformation operator, we have shown that the general form of $\tau$ 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 $\tau$ 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 $x\to0$ and $q\to1$, simultaneously.
Keywords: $q$-deformation; $\tau$ function; Gauge transformation operator; $q$-KP hierarchy; $q$-cKP hierarchy.
Received: January 27, 2006; in final form April 28, 2006; Published online June 13, 2006
Bibliographic databases:
Document Type: Article
Language: English
Citation: Jingsong He, Yinghua Li, Yi Cheng, “$q$-Deformed KP Hierarchy and $q$-Deformed Constrained KP Hierarchy”, SIGMA, 2 (2006), 060, 32 pp.
Citation in format AMSBIB
\Bibitem{HeLiChe06}
\by Jingsong He, Yinghua Li, Yi Cheng
\paper $q$-Deformed KP Hierarchy and $q$-Deformed Constrained KP Hierarchy
\jour SIGMA
\yr 2006
\vol 2
\papernumber 060
\totalpages 32
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\crossref{https://doi.org/10.3842/SIGMA.2006.060}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889234733}
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  • This publication is cited in the following 44 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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