相关论文: Toda lattice realization of integrable hierarchies

We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a subhierarchy of the 2D Toda lattice defined by imposing a constraint to the Lax operators of the latter. The 2D Toda lattice with the…

We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates…

Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…

We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B^+(n) of…

A pedagogical presentation of integrable models with special reference to the Toda lattice hierarchy has been attempted. The example of the KdV equation has been studied in detail, beginning with the infinite conserved quantities and going…

We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…

The superintegrability of the non-periodic Toda lattice is explained in the framework of systems written in action-angles coordinates. Moreover, a simpler form of the first integrals is given.

We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.

We give a representation--theoretic interpretation of recent discovered coupled soliton equations using vertex operators construction of affinization of not simple but quadratic Lie algebras. In this setup we are able to obtain new…

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.

A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…

Applying recent ideas of Carlet, Dubrovin and Zhang (to appear), who, following a suggestion of Eguchi and Yang (hep-th/9407134), study the logarithm of the Lax operator of the Toda lattice, we show that the equivariant Toda lattice…

The Toda hierarchy refers to a family of integrable flows on Jacobi operators that have many applications in mathematics and physics. We demonstrate carefully that an alternative characterization of the Toda hierarchy using cocycle maps is…

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and…

We propose a new integrable N=2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax--pair…

In this paper, we construct the additional $W$-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new…

Integrable cut-off constraints for semidiscrete Toda lattice are studied in this paper. Lax presentation for semidiscrete analog of the $C$-series Toda lattice is obtained. Nonlocal variables that allow to express symmetries of the infinite…

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…

Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of…