Related papers: Multi-component Toda lattice hierarchy
In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential…
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear…
We discuss the generic definition of the $\tau$ function for the arbitrary Hamiltonian system. The different approaches concerning the deformations of the curves and surfaces are compared. It is shown that the Baker-Akhiezer function for…
We study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of bilinear identities, which we show to be equivalent to the Pfaff…
We prove separation of variables for the most general (Dn type) periodic Toda lattice with 2x2 Lax matrix. It is achieved by finding proper normalisation for the corresponding Baker-Akhiezer function. Separation of variables for all other…
In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of…
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 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…
Previous results on quasi-classical limit of the KP hierarchy and its W-infinity symmetries are extended to the Toda hierarchy. The Planck constant $\hbar$ now emerges as the spacing unit of difference operators in the Lax formalism. Basic…
We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time $t_0=x$. It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this…
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
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…
It is well-known that the partition function of the unitary ensembles of random matrices is given by a tau-function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are tau-functions of the Pfaff lattice…
The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice…
In this paper, the authors investigate the case of discrete multiple orthogonal polynomials with two weights on the step line, which satisfy Pearson equations. The discrete multiple orthogonal polynomials in question are expressed in terms…
We consider a (2+1)-dimensional Toda-like chain which can be viewed as a two-dimensional generalization of the Wu-Geng model and which is closely related to the two-dimensional Volterra, two-dimensional Toda and relativistic Toda lattices.…
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which…
In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated…
We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times…
In this paper an approach to generate multi-dimensionally consistent $N$-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained…