Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (5): 1602-1615.

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The $s$-th Generalized Super KP Hierarchy: From One Component to Multi-Components

Huizhan Chen()   

  1. School of Mathematics, China University of Mining and Technology, Jiangsu Xuzhou 221116
  • Received:2024-10-18 Revised:2025-04-14 Online:2025-10-26 Published:2025-10-14
  • Supported by:
    Fundamental Research Funds for the Central Universities(JSX250005)

Abstract:

In this paper, a generalized system of the super KP hierarchy of Kac-van de Leur, $s$-th generalized super KP hierarchy, is considered. We characterize the $s$-th generalized super KP hierarchy in super fermionic Fock space using Clifford super algebra and infinite-dimensional Lie superalgebra of type A, which is defined as an identity in terms of tau functions. Using the super boson-fermion correspondence of type A, the image of the $s$-th generalized super KP hierarchy in super bosonic Fock space is given, which is a system of partial differential equations with super variables. Based on this, we give the super Hirota bilinear identity and derive the KP equation and super KP equation from it. Finally, this system is generalized to the multi-component case.

Key words: $s$-th generalized super KP hierarchy, infinite-dimensional Lie superalgebra, super boson-fermion correspondence of type A, KP equation, super KP equation

CLC Number: 

  • O411.1
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