Kadomtsev-Petviashvili hierarchies of types B and C
A. Zabrodin

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 -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.
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