Abstract

This is a short review of the Kadomtsev–Petviashvili hierarchies of types \(\mathrm{B}\) and \(\mathrm{C}\). The main objects are the \(L\) operator, the wave operator, the auxiliary linear problems for the wave function, the bilinear identity for the wave function, and the tau function. All of them are discussed in the paper. Connections with the usual (type-\(\mathrm{A}\)) Kadomtsev–Petviashvili hierarchy are clarified. Examples of soliton solutions and the dispersionless limit of the hierarchies are also considered.

中文翻译：

---

B 型和 C 型的 Kadomtsev-Petviashvili 层次结构

摘要

这是对\(\mathrm{B}\)和\(\mathrm{C}\)类型的 Kadomtsev–Petviashvili 层次结构的简短回顾。主要对象是\(L\)算子、波算子、波函数的辅助线性问题、波函数的双线性恒等式和tau函数。所有这些都在论文中进行了讨论。与通常的 (type- \(\mathrm{A}\) ) Kadomtsev–Petviashvili 层次结构的联系得到了澄清。还考虑了孤子解和层次结构的无色散限制的例子。