相关论文: Tau-functions and Dressing Transformations for Zer…

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit…

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the…

We introduce a single tau function that represents the CKP hierarchy into a generalized Hirota "bilinear" equation. The actions on the tau function by additional symmetries for the hierarchy are calculated, which involve strictly more than…

Yang-Baxter integrable dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models are considered on the torus in their simplest physical regimes. A combination of boundary conditions $(h,v)$ is applied in the horizontal and vertical directions…

We study a generalization of $T_N$-configurations, called the $\tau_N$-configurations, for constructing certain irregular solutions of some nonlinear diffusion systems by the method of convex integration. We construct some polyconvex…

Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite…

We study explicit formula (suggested by Gamayun, Iorgov, Lisovyy) for Painlev\'e III($D_8$) $\tau$ function in terms of Virasoro conformal blocks with central charge $1$. The Painlev\'e equation has two types of bilinear forms, we call them…

We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which…

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve these are conjectured to be the q-difference Painlev\'e…

Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic…

The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d…

A family of polynomial \tau-functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra \g of type A_1^{(1)}. These \tau-functions are given…

The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux transforms for operators L(t) flowing according to the Toda lattice. Each element of the null-space $L(t)-z$ specifies a factorization for all t and thus a…

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to…

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary…

We consider abelian twisted loop Toda equations associated with the complex general linear groups. The Dodd--Bullough--Mikhailov equation is a simplest particular case of the equations under consideration. We construct new soliton solutions…

We introduce a novel approach for computing the twist operator correlators (TOC) in two-dimensional conformal field theories (2d CFT) and the closely related isomonodromic tau functions. The method stems from the formal path integral…

We have recently solved the inverse spectral problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations…

Partition functions often become \tau-functions of integrable hierarchies, if they are considered dependent on infinite sets of parameters called time variables. The Hurwitz partition functions Z = \sum_R…

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\tau$. More specifically, we define and study two categories $\mathcal{E}_{\tau}$ and $\mathcal{C}_{\tau}$ of…