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Darboux Transformations for SUSY Integrable Systems
Q. P. Liu, Manuel Manas
Several types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered. We also prese…
Vectorial Ribaucour Transformations for the Lame Equations
Q. P. Liu, Manuel Manas
The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vector…
Discrete Levy Transformations and Casorati Determinant Solutions of Quadrilateral Lattices
Q. P. Liu, Manuel Manas
Sequences of discrete Levy and adjoint Levy transformations for the multidimensional quadrilateral lattices are studied. After a suitable number of iterations we show how all the r…
On the Integrable Hierarchies Associated With N=2 Super Algebra
Q. P. Liu
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 t…
Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System
Q. P. Liu, Manuel Mañas
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at le…
Vectorial Darboux Transformations for the Kadomtsev-Petviashvili Hierarchy
Q. P. Liu, M. Manas
We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae fo…
Fully Supersymmetric Hierarchies From A Energy Dependent Super Hill Operator
Q. P. Liu
A super Hill operator with energy dependent potentials is proposed and the associated integrable hierarchy is constructed explicitly. It is shown that in the general case, the resu…
Darboux Transformation for the Manin-Radul Supersymmetric KdV equation
Q. P. Liu, M. Manas
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…
Crum Transformations and Wronskian Type Solutions for Supersymmetric KdV equation
Q. P. Liu, M. Manas
Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained…