q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
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DOI：
10.3842/sigma.2006.060
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发表时间：
2006-06
影响因子：
0.9
通讯作者：
Jingsong He;Yinghua Li;Yi Cheng
中科院分区：
文献类型：
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作者：
Jingsong He;Yinghua Li;Yi Cheng
利用规范变换算符的行列式表示，我们证明了q-KP族的τ函数的一般形式是一个q-变形的广义Wronskian，其中包括作为特例的q-变形的Wronskian.在此基础上，我们研究了q-变形约束KP（q-cKP）族，即q-KP族的l-约束。与普通的约束KP（cKP）族类似，q-cKP族的一大类解可以用满足一组常系数线性q-偏微分方程的函数的q-变形Wronskian行列式表示.我们得到了这些功能所施加的约束的附加条件。特别地，给出了q-形变对q-KP族中最简单的tau函数的单q-孤子和单分量q-cKP族中多q-孤子的影响，以及它们对x和q的依赖关系.最后，我们观察到当x -> 0和q -> 1时，q-孤子同时趋于KP方程的通常孤子。
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 -> 0 and q -> 1, simultaneously.