Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super Bäcklund transformation and is further used to obtain N super soliton solutions. PACS: 02.30.Ik PACS: 12.60.Jv mohsin [email protected] On study leave from PRD (PINSTECH) Islamabad, Pakistan mhassa...

We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we ...

In this article, the Darboux transformation for the non-isospectral AKNS hierarchy is constructed. We show that the Darboux transformation for the non-isospectral AKNS hierarchy is not an auto-Bäcklund transformation, because the integral constants of the hierarchy will be changed after the transformation. The transform rule of the integral constants will be also derived. By this means, the sol...

A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n ≥ 2. New examples of quasi-exactly ...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

In this Letter, we present the third kind of Darboux transformation of the classical Boussinesq system, and discuss its relationship with the two basic Darboux transformations. By applying the Darboux transformations, we obtain the solutions of multiple soliton interactions, including overtaking and head-on collisions.  2001 Published by Elsevier Science B.V.

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generali...

STABILITY AND SENSITIVITY OF DARBOUX TRANSFORMATION WITHOUT PARAMETER M. ISABEL BUENO AND FROILÁN M. DOPICO Abstract. The monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. Darboux transformation without parameter changes a monic Jacobi matrix associa...