279 research outputs found

### On Discrete Symmetries of the Multi-Boson KP Hierarchies

We show that the multi-boson KP hierarchies possess a class of discrete
symmetries linking them to the discrete Toda systems. These discrete symmetries
are generated by the similarity transformation of the corresponding Lax
operator. This establishes a canonical nature of the discrete transformations.
The spectral equation, which defines both the lattice system and the
corresponding Lax operator, plays a key role in determining pertinent symmetry
structure. We also introduce a concept of the square-root lattice leading to a
family of new pseudo-differential operators with covariance under additional
B\"{a}cklund transformations.Comment: 11 pgs, LaTeX, IFT-P/75/93, UICHEP-TH/93-1

### Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation

We present a new form of the multi-boson reduction of KP hierarchy with Lax
operator written in terms of boson fields abelianizing the second Hamiltonian
structure. This extends the classical Miura transformation and the
Kupershmidt-Wilson theorem from the (m)KdV to the KP case. A remarkable
relationship is uncovered between the higher Hamiltonian structures and the
corresponding Miura transformations of KP hierarchy, on one hand, and the
discrete integrable models living on {\em refinements} of the original lattice
connected with the underlying multi-matrix models, on the other hand. For the
second KP Hamiltonian structure, worked out in details, this amounts to finding
a series of representations of the nonlinear \hWinf algebra in terms of
arbitrary finite number of canonical pairs of free fields.Comment: 12 pgs, (changes in abstract, intro and outlook+1 ref added). LaTeX,
BGU-94 / 1 / January- PH, UICHEP-TH/94-

### On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models

Invariance under non-linear ${\sf {\hat W}}_{\infty}$ algebra is shown for
the two-boson Liouville type of model and its algebraic generalizations, the
extended conformal Toda models. The realization of the corresponding generators
in terms of two boson currents within KP hierarchy is presented.Comment: 10 pgs, LaTeX, IFT-P.038/9

### Manifestly Supersymmetric Lax Integrable Hierarchies

A systematic method of constructing manifestly supersymmetric
$1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the
Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy
equations being eigenfunction equations are shown to be automatically invariant
under the (extended) supersymmetry. The supersymmetric Lax models existing in
the literature are found to be contained (up to a gauge equivalence) in our
formalism.Comment: LaTeX, 10 pg

### The sAKNS Hierarchy

We study, systematically, the properties of the supersymmetric AKNS (sAKNS)
hierarchy. In particular, we discuss the Lax representation in terms of a
bosonic Lax operator and some special features of the equations and construct
the bosonic local charges as well as the fermionic nonlocal charges associated
with the system starting from the Lax operator. We obtain the Hamiltonian
structures of the system and check the Jacobi identity through the method of
prolongation. We also show that this hierarchy of equations can equivalently be
described in terms of a fermionic Lax operator. We obtain the zero curvature
formulation as well as the conserved charges of the system starting from this
fermionic Lax operator which suggests a connection between the two. Finally,
starting from the fermionic description of the system, we construct the soliton
solutions for this system of equations through Darboux-Backlund transformations
and describe some open problems.Comment: LaTeX, 16 pg

### Supersymmetry for integrable hierarchies on loop superalgebras

The algebraic approach is employed to formulate N=2 supersymmetry
transformations in the context of integrable systems based on loop
superalgebras $\hat{\rm sl}(p+1,p), p \ge 1$ with homogeneous gradation. We
work with extended integrable hierarchies, which contain supersymmetric AKNS
and Lund-Regge sectors.
We derive the one-soliton solution for $p=1$ which solves positive and
negative evolution equations of the N=2 supersymmetric model.Comment: Latex, 21 page

### Compatible Poisson Structures of Toda Type Discrete Hierarchy

An algebra isomorphism between algebras of matrices and difference operators
is used to investigate the discrete integrable hierarchy. We find local and
non-local families of R-matrix solutions to the modified Yang-Baxter equation.
The three R-theoretic Poisson structures and the Suris quadratic bracket are
derived. The resulting family of bi-Poisson structures include a seminal
discrete bi-Poisson structure of Kupershmidt at a special value.Comment: 22 pages, LaTeX, v3: Minor change

### Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies

The discrete models of the Toda and Volterra chains are being constructed out
of the continuum two-boson KP hierarchies. The main tool is the discrete
symmetry preserving the Hamiltonian structure of the continuum models. The
two-boson currents of KP hierarchy are being associated with sites of the
corresponding chain by successive actions of discrete symmetry.Comment: 12 pgs, LaTeX, IFT-P.041/9

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