Related papers: CKP Hierarchy, Bosonic Tau Function and Bosonizati…
We discuss the Hirota bilinear equation for the CKP hierarchy introduced by Date, Jimbo, Kashiwara and Miwa in J. Phys. Soc. Japan. 50(11), 3813-3818 (1981), and its algebraic properties. We review in parallel the two bosonizations of the…
The CKP tau function has been an important topic in mathematical physics. In this paper, the inverse of vacuum expectation value of exponential of certain bosonic fields, is showed to be the CKP tau function given by Chang and Wu, in the…
In this paper we generalize the fermionic approach to the KP hierarchy sudgested in the papers of Kyoto school 1981-1984 (Sato,Jimbo, Miwa...). The main idea is that the components of the intertwiningoperators are in some sense a…
We present a formula for the connected \(n\)-point functions of a tau-funtion of the BKP hierarchy by embedding BKP hierarchy into KP hierarchy. This formula is different from the one given by Wang and Yang. We prove that these two formulae…
We construct all polynomial tau-functions of the BKP, DKP and MDKP hierarches.
In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s_\lambda(t)$ by certain shifts of arguments. In the present…
We give 4 formulations of the Modified KP hierarchy and show that they are equivalent. We also discuss the reductions of the MKP hierarchy to the modified $n$-KdV hierarchies. As a byproduct, we find an astonishingly simple explicit…
We prove existence of the tau-function for the multi-component CKP hierarchy and find how it is related to the tau-function of the multi-component KP hierarchy.
In this paper we discuss the second bosonization of the Hirota bilinear equation for the CKP hierarchy introduced by Date, Jimbo, Kashiwara and Miwa. We show that there is a second, untwisted, Heisenberg action on the Fock space, in…
We derive a formula for the connected $n$-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679]. Moreover, we…
The first part of the paper is devoted to two descriptions of all polynomial tau-functions of the KP hierarchy: by a generalized Jacobi-Trudy formula, and a generalized Giambelli formula. We use the latter formula in the second part to…
In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies…
The CKP hierarchy is one important sub-hierarchy of the KP hierarchy, which is quite special due to its tau function. Here we construct the tau functions for the constrained CKP hierarchy…
We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial…
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B) which can be regarded as a discretization of the BKP hierarchy. We introduce the tau-function of the B-Toda hierarchy and obtain the bilinear…
Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction…
In this paper, free Bosons are used to study some integrable properties of the CKP hierarchy, from the aspects of tau functions. Firstly, the modified CKP hierarchy is constructed by using free Bosons and the corresponding Lax structure is…
The $2M$-boson representations of KP hierarchy are constructed in terms of $M$ mutually independent two-boson KP representations for arbitrary number $M$. Our construction establishes the multi-boson representations of KP hierarchy as…
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…
We survey several results connecting combinatorics and Wronskian solutions of the KP equation, contextualizing the successes of a recent approach introduced by Kodama, et. al. We include the necessary combinatorial and analytical background…