Kadomtsev-Petviashvili hierarchies of types B and C

TL;DR

This paper reviews the KP hierarchies of types B and C, discussing their main objects, connections to type A, soliton solutions, and dispersionless limits.

Contribution

It provides a comprehensive overview of the KP hierarchies of types B and C, clarifying their structures and relations to the classical KP hierarchy.

Findings

Clarification of the L-operator, wave operator, and tau-function for types B and C

Examples of soliton solutions for these hierarchies

Analysis of the dispersionless limit of the hierarchies

Abstract

This is a short review of the Kadomtsev-Petviashvili hierarchies of types B and 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. The connections with the usual Kadomtsev-Petviashvili hierarchy (of the type A) are clarified. Examples of soliton solutions and the dispersionless limit of the hierarchies are also considered.