243 research outputs found
Pfaffian Solutions for the Manin-Radul-Mathieu SUSY KdV and SUSY sine-Gordon Equations
We reduce the vectorial binary Darboux transformation for the Manin-Radul
supersymmetric KdV system in such a way that it preserves the
Manin-Radul-Mathieu supersymmetric KdV equation reduction. Expressions in terms
of bosonic Pfaffians are provided for transformed solutions and wave functions.
We also consider the implications of these results for the supersymmetric
sine-Gordon equation.Comment: 10 pages, LaTeX2e with AMSLaTeX and Babel package
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
Nonlinear superposition formula for N=1 supersymmetric KdV Equation
In this paper, we derive a B\"{a}cklund transformation for the supersymmetric
Kortweg-de Vries equation. We also construct a nonlinear superposition formula,
which allows us to rebuild systematically for the supersymmetric KdV equation
the soliton solutions of Carstea, Ramani and Grammaticos.Comment: 6 pages, LaTeX, everthing is reformed into super field
Decouple a coupled KdV system of Nutku and O\~{g}uz
A coupled KdV system with a free parameter proposed by Nutku and O\~{g}uz is
considered. It is shown that the system passes the WTC's Painlev\'{e} test for
arbitrary value of the parameter. A further analysis yields that the parameter
can be scaled away and the system can be decoupled.Comment: LaTeX 209, 4 page
The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations
It is shown that two different supersymmetric extensions of the Harry Dym
equation lead to two different negative hierarchies of the supersymmetric
integrable equations. While the first one yields the known even supersymmetric
Hunter - Saxton equation, the second one is a new odd supersymmetric Hunter -
Saxton equation. It is further proved that these two supersymmetric extensions
of the Hunter - Saxton equation are reciprocally transformed to two different
supersymmetric extensions of the Liouville equation.Comment: typos corrected and references added. To appear in Phys.Lett
Darboux Transformation for the Manin-Radul Supersymmetric KdV equation
In this paper we present a vectorial Darboux transformation, in terms of
ordinary determinants, for the supersymmetric extension of the Korteweg-de
Vries equation proposed by Manin and Radul. It is shown how this transformation
reduces to the Korteweg-de Vries equation. Soliton type solutions are
constructed by dressing the vacuum and we present some relevant plots.Comment: 14 pp, 2 figures, AMS-LaTeX, to appear in Phys. Lett.
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.
A supersymmetric Sawada-Kotera equation
A new supersymmetric equation is proposed for the Sawada-Kotera equation. The
integrability of this equation is shown by the existence of Lax representation
and infinite conserved quantities and a recursion operator.Comment: 9 pages, replaced with the version
The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated algebra
For any two arbitrary positive integers `' and `', using the --th
KdV hierarchy and the --th KdV hierarchy as building blocks, we are able
to construct another integrable hierarchy (referred to as the --th KdV
hierarchy). The --algebra associated to the \shs\, of the --th KdV
hierarchy (called algebra) is isomorphic via a Miura map to the direct
sum of --algebra, --algebra and an additional current
algebra. In turn, from the latter, we can always construct a representation of
--algebra.Comment: 26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43,
revised version with addition
From nonassociativity to solutions of the KP hierarchy
A recently observed relation between 'weakly nonassociative' algebras A (for
which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent
variable in the middle nucleus A' of A) is recalled. For any such algebra there
is a nonassociative hierarchy of ODEs, the solutions of which determine
solutions of the KP hierarchy. In a special case, and with A' a matrix algebra,
this becomes a matrix Riccati hierarchy which is easily solved. The matrix
solution then leads to solutions of the scalar KP hierarchy. We discuss some
classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and
Quantum Symmetries', Prague, 15-17 June 200
- …