修正离散KP系列的流方程

该文主要研究修正离散KP系列的流方程问题,给出流方程的一般表示形式.     

A General Formula of Flow Equations for Harry-Dym Hierarchy

In this paper, we derive a general formula of the flow equtions for the Harry-Dym hierarchy. And three applications in n-reduction, (2+1)-dimensional generalization, and Kupershmidt reduction, are considered.     

约束离散KP方程族的完全Virasoro对称

首先讨论了约束离散KP可积方程族一种等价形式:差分算子的商.接下来,利用这种新的描述形式,构造了约束离散KP方程族的完全Virasoro对称.     

Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies

In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are explicitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and CTL constraints. Also the connections with the corresponding additional symmetries are investigated: the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.     

Gauge Transformation for BCr-KP Hierarchy and Its Compatibility with Additional Symmetry

The BCr-KP hierarchy is an important sub-hierarchy of the KP hierarchy. In this paper, the BCr-KP hierarchy is investigated from three aspects. Firstly, we study the gauge transformation for the BCr-KP hierarchy.Different from the KP hierarchy, the gauge transformation must keep the constraint of the BCr-KP hierarchy. Secondly,we study the gauge transformation for the constrained BCr-KP hierarchy. In this case, the constraints of the Lax operator must be invariant under the gauge transformation. At last, the compatibility between the additional symmetry and the gauge transformation for the BCr-KP hierarchy is explored.     

BKP 与CKP 可积系列的递归算子

借助于新引进的算子B, 本文给出了BKP 与CKP 可积系列约束条件在其Lax 算子L中的动力学变量上的具体体现, 即奇数阶动力学变量u_2k+1 能被偶数阶动力学变量u_2k 显式表达. 同时本文给出了BKP 与CKP 可积系列的流方程以及(2n + 1)- 约化下递归算子的统一公式, 揭示了BKP 可积系列和CKP 可积系列的重要区别. 作为例子, 本文给出了BKP 与CKP 可积系列在3- 约化下的递归算子的显式表示, 并验证了u₂ 的t₁ 流通过递归算子的确可以产生u₂ 的t₇ 流, 该流方程与3- 约化下产生的对应流方程是一致的.