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Darboux Transformation for Supersymmetric KP Hierarchies
Q. P. Liu, Manuel Manas
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 hierarchi…
Pfaffian Solutions for the Manin-Radul-Mathieu SUSY KdV and SUSY sine-Gordon Equations
Q. P. Liu, Manuel Manas
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 equat…
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…
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…
Painlevé Analysis and Exact Solutions of a Modified Boussinesq Equation
Q. P. Liu
We consider a modified Boussinesq type equation. The Painlevé test of the WTC method is performed for this equation and it shows that the equation has weak Painlevé property. Some…
Supersymmetric Harry Dym Type Equations
Q. P. Liu
A supersymmetric version is proposed for the well known Harry Dym system. A general class super Lax operator which leads to consistent equations is considered.