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

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dc.creatorHe, Jingsong
dc.creatorLi, Yinghua
dc.creatorCheng, Yi
dc.date2006-06-14
dc.date2006-06-15
dc.date.accessioned2026-07-07T09:34:40Z
dc.date.available2026-07-07T09:34:40Z
dc.descriptionUsing 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 $x\to 0$ and $q\to 1$, simultaneously.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/nlin/0606039
dc.identifierhttp://arxiv.org/abs/nlin/0606039
dc.identifierSIGMA 2 (2006), 060, 32 pages
dc.identifierdoi:10.3842/SIGMA.2006.060
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159572
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.titleq-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
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