Kadomtsev-Petviashvili hierarchies of types B and C

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.

26 pages, no figures. arXiv admin note: text overlap with arXiv:2012.04482

References in corpus (3)

• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• Kadomtsev-Petviashvili turning points and CKP hierarchy
• BKP and CKP revisited: The odd KP system

Cited by in corpus (1)

• Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation