254 research outputs found
On the Integrable Hierarchies Associated With N=2 Super Algebra
A new Lax operator is proposed from the viewpoint of constructing the
integrable hierarchies related with N=2 super algebra. It is shown that
the Poisson algebra associated to the second Hamiltonian structure for the
resulted hierarchy contains the N=2 super Virasoro algebra as a proper
subalgebra. The simplest cases are discussed in detail. In particular, it is
proved that the supersymmetric two-boson hierarchy is one of N=2 supersymmetric
KdV hierarchies. Also, a Lax operator is supplied for one of N=2 supersymmetric
Boussinesq hierarchies.Comment: 11 pages, AMS-LaTex, to appear in Phys. Lett.
Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System
We show that the 2-matrix string model corresponds to a coupled system of
-dimensional KP and modified KP (\KPm) integrable equations subject to a
specific ``symmetry'' constraint. The latter together with the
Miura-Konopelchenko map for \KPm are the continuum incarnation of the matrix
string equation. The \KPm Miura and B\"{a}cklund transformations are natural
consequences of the underlying lattice structure. The constrained \KPm system
is equivalent to a -dimensional generalized KP-KdV hierarchy related to
graded . We provide an explicit representation of this
hierarchy, including the associated -algebra of the second
Hamiltonian structure, in terms of free currents.Comment: 12+1 pgs., LaTeX, preprint: BGU-94 / 15 / June-PH, UICHEP-TH/94-
Crum Transformations and Wronskian Type Solutions for Supersymmetric KdV equation
Darboux transformation is reconsidered for the supersymmetric KdV system. By
iterating the Darboux transformation, a supersymmetric extension of the Crum
transformation is obtained for the Manin-Radul SKdV equation, in doing so one
gets Wronskian superdeterminant representations for the solutions. Particular
examples provide us explicit supersymmetric extensions, super solitons, of the
standard soliton of the KdV equation. The KdV soliton appears as the body of
the super soliton.Comment: 13 pp, AMS-LaTe
Darboux Transformation for Supersymmetric KP Hierarchies
We construct Darboux transformations for the super-symmetric KP hierarchies
of Manin--Radul and Jacobian types. We also consider the binary Darboux
transformation for the hierarchies. The iterations of both type of Darboux
transformations are briefly discussed.Comment: 14 pages, LaTeX2e with amsmath,amssymb,amsthm and geometry packages.
In this new version we consider both the Manin-Radul and the Jacobian SKP
hierachies and we show how the elementary Darboux transformation composed
with a reversion of signs in the fermionic times constitute a proper
transformation of these hierarchie
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
On the constrained KP hierarchy
An explanation for the so-called constrained hierarhies is presented by
linking them with the symmetries of the KP hierarchy. While the existence of
ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP
hierarchy to the KdV hierarchies, the existence of additional symmetries allows
to reduce KP to the constrained KP.Comment: 7pp, LaTe
On symmetries of KdV-like evolution equations
The -dependence of the symmetries of (1+1)-dimensional scalar
translationally invariant evolution equations is described. The sufficient
condition of (quasi)polynomiality in time of the symmetries of evolution
equations with constant separant is found. The general form of time dependence
of the symmetries of KdV-like non-linearizable evolution equations is
presented.Comment: LaTeX, 8 pages, no figures, very minor change
Virasoro Symmetry of Constrained KP Hierarchies
Additional non-isospectral symmetries are formulated for the constrained
Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of
compatibility of additional symmetries with the underlying constraints is
solved explicitly for the Virasoro part of the additional symmetry through
appropriate modification of the standard additional-symmetry flows for the
general (unconstrained) KP hierarchy. We also discuss the special case of \cKP
--truncated KP hierarchies, obtained as Darboux-B\"{a}cklund orbits of initial
purely differential Lax operators. The latter give rise to Toda-lattice-like
structures relevant for discrete (multi-)matrix models. Our construction
establishes the condition for commutativity of the additional-symmetry flows
with the discrete Darboux-B\"{a}cklund transformations of \cKP hierarchies
leading to a new derivation of the string-equation constraint in matrix models.Comment: LaTeX, 11 pg
Tri-hamiltonian vector fields, spectral curves and separation coordinates
We show that for a class of dynamical systems, Hamiltonian with respect to
three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are
provided by the common roots of a set of bivariate polynomials. These
polynomials, which generalise those considered by E. Sklyanin in his
algebro-geometric approach, are obtained from the knowledge of: (i) a common
Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu
P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to
its symplectic leaves. The frameworks is applied to Lax equations with spectral
parameter, for which not only it unifies the separation techniques of Sklyanin
and of Magri, but also provides a more efficient ``inverse'' procedure not
involving the extraction of roots.Comment: 49 pages Section on reduction revisite
From dispersionless to soliton systems via Weyl-Moyal like deformations
The formalism of quantization deformation is reviewed and the Weyl-Moyal like
deformation is applied to systematic construction of the field and lattice
integrable soliton systems from Poisson algebras of dispersionless systems.Comment: 26 page
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