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

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

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 WnW_n Algebra

A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N=2 super $W_n$ 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 WW algebra

For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV hierarchy). The $W$--algebra associated to the \shs\, of the $(n,m)$--th KdV hierarchy (called $W(n,m)$ algebra) is isomorphic via a Miura map to the direct sum of $W_m$--algebra, $W_{n+m}$--algebra and an additional $U(1)$ current algebra. In turn, from the latter, we can always construct a representation of $W_\infty$--algebra.Comment: 26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43, revised version with addition