论文标题
在$（t_2，t_3） - $ zakharov-shabat方程的广义kadomtsev-petviashvili层次结构
On $(t_2,t_3)-$Zakharov-Shabat equations of generalized Kadomtsev-Petviashvili hierarchies
论文作者
论文摘要
我们回顾了在几个非标准环境中KP层次结构的集成。具体而言，我们在以下关联差分代数中考虑KP：配备了nilpotent推导的代数；配备有推导的功能代数，该派生概括了梯度运算符；四元基金值函数的代数；一个不同的谎言代数；配备固定差分的多项式代数； Moyal代数。在所有这些情况下，我们都可以制定和解决KP层次结构的库奇问题。同样，在每种情况下，我们都会得出不同的Zakharov-Shabat $（T_2，T_3）$ - 方程 - 即，不同的Kadomtsev-Petviashvili方程式 - 我们证明了来自相应KP HierArchy的解决方案的存在。
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation; an algebra of functions equipped with a derivation that generalizes the gradient operator; an algebra of quaternion-valued functions; a differential Lie algebra; an algebra of polynomials equipped with the Pincherle differential; a Moyal algebra. In all these cases we can formulate and solve the Cauchy problem of the KP hierarchy. Also, in each of these cases we derive different Zakharov-Shabat $(t_2,t_3)$-equations -- that is, different Kadomtsev-Petviashvili equations -- and we prove existence of solutions arising from solutions to the corresponding KP hierarchy.
