Related papers: B\"acklund-Darboux Transformations for Super KdV T…
Baecklund-Darboux transformations are closely related to the integrability and symmetry problems. For the generalized Baecklund-Darboux transformation (GBDT), we consider conservation laws, rational extensions and bispectrality. We use the…
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B.…
The $\hat B_n^{(1)}$-hierarchy is constructed from the standard splitting of the affine Kac-Moody algebra $\hat B_n^{(1)}$, the Drinfeld-Sokolov $\hat B_n^{(1)}$-KdV hierarchy is obtained by pushing down the $\hat B_n^{(1)}$-flows along…
We construct the supersymmetric extensions of the Darboux-Backlund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators…
Assuming that there exist at least two fermionic parameters, the classical N= 1 supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are…
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations,…
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary…
The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well…
Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained for the Manin-Radul SKdV equation, in doing so one gets…
We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on…
We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a…
In this paper, based on the regular KdV system, we study negative order KdV (NKdV) equations about their Hamiltonian structures, Lax pairs, infinitely many conservation laws, and explicit multi-soliton and multi-kink wave solutions thorough…
We construct a deformation quantized version (ncKdV) of the KdV equation which possesses an infinite set of conserved densities. Solutions of the ncKdV are obtained from solutions of the KdV equation via a kind of Seiberg-Witten map. The…
A systematic construction for supersymmetric negative graded (non-local) flows for mKdV and KdV based on $sl(2,1)$ with a principal gradation is proposed in this paper. We show that smKdV and sKdV can be mapped onto each other through a…
Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides…
This paper studies Manin-Radul supersymmetric KP hierarchy (MR-SKP) in three related aspects: (i) We find an infinite set of additional (``ghost'') symmetry flows spanning the same (anti-)commutation algebra as the ordinary MR-SKP flows;…
Generalized B\"acklund-Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of direct and inverse problems of Weyl-Titchmarsh theory. During explicit solving of the…
The relation between the Darboux transformation and the solutions of the full Kostant Toda lattice is analyzed. The discrete Korteweg de Vries equation is used to obtain such solutions and the main result of [1] is extended to the case of…
We present a non-isospectral GBDT version of B\"acklund-Darboux transformation for the gravitational and $\sigma$-model equations. New families of explicit solutions correspond to the case of GBDT with non-diagonal generalized matrix…
The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure.…