Related papers: Backlund Transformation for Integrable Hierarchies…
In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versions (using Darboux transformations) of the spectral problems…
We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen,…
This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A B\"acklund transformation is derived for the Yang…
We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the…
The construction of type II Backlund transformation for the sine-Gordon and the Tzitzeica-Bullough-Dodd models are obtained from gauge transformation. An infinite number of conserved quantities are constructed from the defect matrices. This…
We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis,…
Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
For the integrable case of the discrete self-trapping (DST) model we construct a Backlund transformation. The dual Lax matrix and the corresponding dual Backlund transformation are also found and studied. The quantum analog of the Backlund…
The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under…
The geometry of an admissible B\"acklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite--dimensional skeleton which is the universal…
This paper gives a new integrable hierarchy of nonlinear evolution equations. The DP equation: $m_t+um_x+3mu_x=0, m=u-u_{xx}$, proposed recently by Desgaperis and Procesi \cite{DP[1999]}, is the first one in the negative hierarchy while the…
We consider a projective transformation and establish the invariants for this transformation group up to order seven. We use the obtained invariants to construct a class of nonlinear evolution equations and identify some symmetry-integrable…
Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified…
Recently a new supersymmetric extension of the KdV hierarchy has appeared in a matrix-model-inspired approach to $2{-}d$ quantum supergravity. Here we prove that this hierarchy is essentially the KdV hierarchy, where the KdV field is now…
A reciprocal transformation for a 3-component Camassa-Holm type system is constructed to connect it with the first negative flow of a generalized MKdV hierarchy, and a bi-Hamiltonian structure for the transformed system is also considered.
In this paper we describe B\"acklund transformations and hierarchies of exact solutions for the fourth Painlev\'e equation (PIV) $${\d^2 w\over\d z^2}={1\over2w}\left(\d w\over\d z\right)^2 + {{3\over2}}w^3 + 4zw^2 +…
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitions. By splitting the problem's solution in two steps, we…
One of the few schemes for obtaining an integrable nonultralocal quantum model is its possible generation from an ultralocal model by a suitable gauge transformation. Applying this scheme we discover two new nonultralocal models, which fit…
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…