论文标题
符号KP，正交KP和BUC层次结构的多项式tau功能
Polynomial tau-functions of the symplectic KP, orthogonal KP and BUC hierarchies
论文作者
论文摘要
本文与B型（BUC层次结构）（BUC层次结构）的符合性KP（SKP），正交KP（OKP）层次结构和通用性角色层次结构的多项式TAU功能有关，这些层次被证明是生成功能的某些组合组合的零模式。通过应用量子场对真空矢量的作用的策略，已经提出了用于符号Schur函数的生成函数，正交Schur函数和广义Q功能。显着的特征是多项式tau功能是某些产生功能系列的系数。此外，就PFAFFIAN的Vandermonde样身份和特性而言，SKP，OKP和BUC层次结构的多项式tau函数分别可以写成确定性和Pfaffian形式。此外，已经讨论了SKP和OKP层次结构的孤子解决方案。
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 canbe written as determinant and Pfaffian forms, respectively. In addition, the soliton solutions of the SKP and OKP hierarchies have been discussed.
