ar X iv : s ol v - in t / 9 90 90 16 v 1 1 6 Se p 19 99 Darboux Transformation and Supersymmetric KP Hierarchy
نویسنده
چکیده
We construct Darboux transformations for the supersymmetric KP hierarchy. We show that the naive candidate does not work due to the pressure of the odd flows,but its composition does give rise to a meaningful Darboux transformation. We also consider the b inary Darboux transformation for the hierarchy. The iterations of both type of Darboux transformations are briefly discussed.
منابع مشابه
ar X iv : s ol v - in t / 9 90 50 05 v 2 1 7 M ay 1 99 9 The KP Hierarchy in Miwa coordinates ∗
A systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay’s identities are obtained. It is shown that in terms of these variables the KP hierarchy gives rise to a Darboux system describing an infinite-dimensional conjugate net.
متن کاملar X iv : s ol v - in t / 9 71 20 09 v 1 1 8 D ec 1 99 7 Canonical Gauge Equivalences of the sAKNS and sTB
We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which turns out to be canonical. We also obtain the Darboux-Bäcklund transformations for the sAKNS hierarchy from these gauge transformations.
متن کاملar X iv : s ol v - in t / 9 90 90 27 v 1 2 6 Se p 19 99 On two aspects of the Painlevé analysis
The Calogero equation is used to illustrate the following two aspects of the Painlevé analysis of PDEs: (i) the singular expansions of solutions around characteristic hypersurfaces are neither single-valued functions of independent variables nor single-valued functionals of data; (ii) the truncated singular expansions not necessarily lead to the simplest, elementary, Bäcklund autotransformation...
متن کاملar X iv : s ol v - in t / 9 70 70 14 v 1 2 7 Ju l 1 99 7 The constrained modified KP hierarchy and the generalized Miura transformations
In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.
متن کاملar X iv : s ol v - in t / 9 70 40 14 v 1 2 1 A pr 1 99 7 Trilinear representation and the Moutard transformation for the Tzitzéica equation
In this paper we present a trilinear form and a Darboux-type transformation to equation (ln v) xy = v − 1/v 2 considered by Tzitzéica in 1910. Soliton solutions are constructed by dressing the trivial solution.
متن کامل