Related papers: Backlund Transformations for Darboux Integrable Di…
We construct a Darboux transformation of a general $su(3)$-valued spin system called the $\Gamma$-spin system. Using this Darboux transformation we derive a recursive formula for the soliton solutions of this spin system. Then using these…
A new integrable lattice system is introduced, and its integrable discretizations are obtained. A B\"acklund transformation between this new system and the Toda lattice, as well as between their discretizations, is established.
As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two…
We study the discretization of Darboux integrable systems. The discretization is done using $x$-, $y$-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
This article encloses the derivation of Darboux solutions for Kaup Kupershmidt equations with their generalization in determinantal form. One of the main focuses of this work is to construct the Backlund transformation for the different…
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 present solutions such as supersolitons and superkinks.
Symmetry of SDYM equations for "physically restricted solution" with hermitian group element $G=G^H$ in representation of Yang is described. Such transformation $D^B$ pass some PRS to the new one of the same kind. Transformation contain…
A Backlund transformation between two hyperbolic Monge-Ampere systems may be described as a certain type of exterior differential system on a 6-dimensional manifold B. The transformation is homogeneous if the group of symmetries of the…
In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion…
We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of…
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…
We construct a Backlund transformation for the Geng-Xue system with the help of reciprocal and gauge transformations. Furthermore, we derive N-Backlund transformation for the Geng-Xue system resorting to Bianchi's permutability. As an…
The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an…
Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple…
We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schr\"odinger type equations. We consider all possible finite reduction groups and construct corresponding Lax operators, Darboux transformations,…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
We develop the Darboux procedure for the case of the two-level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two-level…
A version of the iterated B\"acklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on…
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study…