Related papers: Lax structure and tau function for large BKP hiera…
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 study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition…
In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear…
Using the free fermions technique and bosonization rules we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota-Miwa type are obtained as…
Adler, Shiota and van Moerbeke obtained for the KP and Toda lattice hierarchies a formula which translates the action of the vertex operator on tau--functions to an action of a vertex operator of pseudo-differential operators on wave…
Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as "the coupled KP hierarchy" and "the Pfaff lattice"). Those results are now extended to a Toda version of the DKP hierarchy (tentatively…
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum…
We study the BKP hierarchy and its $n$--reduction, for the case that $n$ is odd. This is related to the principal realization of the basic module of the twisted affine Lie algebra $\hat{sl}_n^{(2)}$. We show that the following two…
In this paper we define a family of systems which have similarities with the Toda lattice. We construct two Lax pair representations and the associate Poisson structures for these systems. These systems lie between the classical Toda…
A construction of general solutions of the \hbar-dependent Toda hierarchy is presented. The construction is based on a Riemann-Hilbert problem for the pairs (L,M) and (\bar L,\bar M) of Lax and Orlov-Schulman operators. This Riemann-Hilbert…
Toda lattice hierarchy and the associated matrix formulation of the $2M$-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working…
We derive an explicit formula for the connected $(n,m)$-point functions associated to an arbitrary diagonal tau-function $\tau_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$ of the 2d Toda lattice hierarchy using fermionic computations and the…
We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax…
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 consider a special class of solutions of the BKP hierarchy which we call $\tau$-functions of hypergeometric type. These are series in Schur $Q$-functions over partitions, with coefficients parameterised by a function of one variable…
In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…
In this paper, we defined a new multi-component BKP hierarchy which takes values in a commutative subalgebra of $gl(N,\mathbb C)$. After this, we give the gauge transformation of this commutative multi-component BKP (CMBKP) hierarchy.…
In this paper, we construct the bilinear identities for the wave functions of an extended B-type Kadomtsev-Petviashvili (BKP) hierarchy, which contains two types of (2+1)-dimensional Sawada-Kotera equation with a self-consistent source…
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…
The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum operators of the corresponding quantum integrable models.…