|
Эта публикация цитируется в 43 научных статьях (всего в 43 статьях)
$q$-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
Аннотация:
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.
Ключевые слова:
$q$-deformation; $\tau$ function; Gauge transformation operator; $q$-KP hierarchy; $q$-cKP hierarchy.
Поступила: 27 января 2006 г.; в окончательном варианте 28 апреля 2006 г.; опубликована 13 июня 2006 г.
Образец цитирования:
Jingsong He, Yinghua Li, Yi Cheng, “$q$-Deformed KP Hierarchy and $q$-Deformed Constrained KP Hierarchy”, SIGMA, 2 (2006), 060, 32 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma88 https://www.mathnet.ru/rus/sigma/v2/p60
|
Статистика просмотров: |
Страница аннотации: | 371 | PDF полного текста: | 68 | Список литературы: | 35 |
|