论文标题
对称离散AKP和BKP方程
Symmetric discrete AKP and BKP equations
论文作者
论文摘要
我们表明，当KP（kadomtsev-petviashvili）$τ$函数允许特殊对称性时，离散的BKP方程可以表示为离散AKP方程的线性组合及其反映的对称形式。因此，离散的AKP和BKP方程可以与这些对称性共享相同的$τ$函数。这种连接扩展到相应离散层次结构中的4维（即高阶）离散AKP和BKP方程。给出了各种明确的$τ$功能的表格，包括hirota的形式，格拉米亚语，卡索拉特语和多项式。研究了由WeierStrass $σ$函数组成的Cauchy矩阵形式的对称$τ$。结果，我们获得具有椭圆系数的离散BKP方程。
We show that when KP (Kadomtsev-Petviashvili) $τ$ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete AKP and BKP equations can share the same $τ$ functions with these symmetries. Such a connection is extended to 4 dimensional (i.e. higher order) discrete AKP and BKP equations in the corresponding discrete hierarchies. Various explicit forms of such $τ$ functions, including Hirota's form, Gramian, Casoratian and polynomial, are given. Symmetric $τ$ functions of Cauchy matrix form that are composed of Weierstrass $σ$ functions are investigated. As a result we obtain a discrete BKP equation with elliptic coefficients.
