论文标题
在Kadomtsev--petviashvili方程的分形集和解决方案上支持的分布
Distributions Supported on Fractal Sets and Solutions to the Kadomtsev--Petviashvili Equation
论文作者
论文摘要
在本说明中，我们将讨论有关原始解决方案的一些最新结果的潜在有趣的扩展，以实现完全集成的偏微分方程。我们将讨论一个家庭分布，这些分布在Riemann Sphere上是全态的，除非在cantor套装或Sierpinski垫圈的单数套装上同型。这些分布使我们能够为kadomtsev--petviashvili方程生成解决方案。这些分布是理性功能家族的局限性，也可以与具有有限数量的双重变性奇异点的表面上的全态线束相关。我们猜想这些分布的子集可用于在某些表面上制定塑形线束的定义，这些表面是同型球形的，除非它们在cantor set或sierpinski垫圈的同型同型同型上在同型同型上变得双重变性。
In this note we will discuss a potentially interesting extension of some recent results on primitive solutions to completely integrable partial differential equations. We will discuss a family distributions that are holomorphic on the Riemann sphere except on the singular sets homeomorphic to a Cantor set or Sierpinski gasket. These distributions allow us to produce solutions to the Kadomtsev--Petviashvili equation. These distributions are limits of families of rational functions that can also be associated with holomorphic line bundles on surfaces with a finite number of doubly degenerate singular points. We conjecture that a subset of these distributions can be used to formulate a definition of a holomorphic line bundle on some surfaces that are homeomorphic to spheres except where they become doubly degenerate on singular sets homeomorphic to a Cantor set or Sierpinski gasket.
