Add to ORKGThe focus of this paper is the extended Toda Lattice hierarchy, an infinite system of partial differential equations arising from the Toda lattice equation. We begin by giving the definition of the extended Toda hierarchy and its explicit bilinear equation, following Takasaki’s construction. We then derive a series of new Fay identities. Finally, we discover a general formula for one type of Fay identity
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy...
We consider the first member of an extended Toda lattice hierarchy. This system of equations is diff...
A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying ...
Using construction of logarithm of a difference operator, we present the Lax pair formalism for cert...
Abstract. In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hiera...
The lattice Gelfand-Dickey hierarchy is a lattice version of the Gelfand-Dickey hierarchy. A special...
We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a su...
Using the matrix-resolvent method and a formula of the second-named author on the $n$-point function...
In this paper we present an analytic and geometric framework for the construction of solutions of th...
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy...
A tower for a (2+1)-dimensional Toda type system is constructed in terms of a series expansion of op...
The intermediate long wave (ILW) hierarchy and its generalization, labelled by a positive integer $N...
Starting from the Toda spectral problem, a new Toda lattice hierarchy of isospectral equations wi...
Starting from the Toda spectral problem, a new Toda lattice hierarchy of isospectral equations with ...
Abstract The aim of this paper is to summarize some recently obtained relations between the Ablowitz...
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy...
We consider the first member of an extended Toda lattice hierarchy. This system of equations is diff...
A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying ...
Using construction of logarithm of a difference operator, we present the Lax pair formalism for cert...
Abstract. In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hiera...
The lattice Gelfand-Dickey hierarchy is a lattice version of the Gelfand-Dickey hierarchy. A special...
We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a su...
Using the matrix-resolvent method and a formula of the second-named author on the $n$-point function...
In this paper we present an analytic and geometric framework for the construction of solutions of th...
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy...
A tower for a (2+1)-dimensional Toda type system is constructed in terms of a series expansion of op...
The intermediate long wave (ILW) hierarchy and its generalization, labelled by a positive integer $N...
Starting from the Toda spectral problem, a new Toda lattice hierarchy of isospectral equations wi...
Starting from the Toda spectral problem, a new Toda lattice hierarchy of isospectral equations with ...
Abstract The aim of this paper is to summarize some recently obtained relations between the Ablowitz...
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy...
We consider the first member of an extended Toda lattice hierarchy. This system of equations is diff...
A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying ...