Plethystic B-type KP and universal character hierarchies

Li, Chuanzhong

doi:10.1007/s10801-021-01066-2

Cited by 6 publications

(1 citation statement)

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“…Ogawa [24] defined a generalized Q-function expressed by the Pfaffian and constructed an integrable UC hierarchy of B-type (BUC hierarchy) characterized by the generalized Q-function. Lately, in the paper [25,26], the author generalized the theory of BUC hierarchy to a coupled and plethystic cases, which can derive coupled and plethystic infinite order nonlinear PDEs.…”

Section: Introductionmentioning

confidence: 99%

Polynomial tau-functions of the symplectic KP, orthogonal KP and BUC hierarchies

Li¹,

Yan²

2022

Preprint

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This paper is concerned with the construction of the polynomial tau-functions of the symplectic KP (SKP), orthogonal KP (OKP) hierarchies and universal character hierarchy of B-type (BUC hierarchy), which are proved as zero modes of certain combinations of the generating functions. By applying the strategy of carrying out the action of the quantum fields on vacuum vector, the generating functions for symplectic Schur function, orthogonal Schur function and generalized Q-function have been presented. The remarkable feature is that polynomial tau-functions are the coefficients of certain family of generating functions. Furthermore, in terms of the Vandermonde-like identity and properties of Pfaffian, it is showed that the polynomial tau-functions of the SKP, OKP and BUC hierarchies can be written as determinant and Pfaffian forms, respectively. In addition, the soliton solutions of the SKP and OKP hierarchies have been discussed.

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Section: Introductionmentioning

confidence: 99%