Related papers: Binary Darboux-Backlund Transformations for the Ma…
A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlev\'{e} analysis and reduction of a binary Darboux…
Elementary Darboux--Laplace transformations for semidiscrete and discrete second order hyperbolic operators are classified. It is proved that in the (semi)-discrete case there are two types of elementary Darboux--Laplace transformations as…
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;…
By applying the higher order Darboux algorithm to an exactly solvable non Hermitian ${\cal{PT}}$ symmetric potential, we obtain a hierarchy of new exactly solvable non Hermitian ${\cal{PT}}$ symmetric potentials with real spectra. It is…
We construct rational extensions of the Darboux-P\"oschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only…
We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
In our previous work \cite{LNS}, we constructed quasi-Casoratian solutions to the noncommutative $q$-difference two-dimensional Toda lattice ($q$-2DTL) equation by Darboux transformation, which we can prove produces the existing Casoratian…
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding…
We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference…
A new form of Darboux-B\"acklund transformation and its higher order form is derived for Derivative Nonlinear Schrodinger Equation(DNLS). The new form arises due to the different form of Lax pair. It is observed that by a special choice of…
It is shown that explicit B\"{a}cklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations…
A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are…
Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials…
A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of…
By demanding consistency of the Legendre transform construction of hyperk\"ahler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperk\"ahler manifold. We apply these results to study the…
We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebro-geometric solutions of these hierarchies.
A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and…
In this paper, we construct a Darboux transformation and the related B\"acklund transformation for the supersymmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is also worked out. We demonstrate that these…
The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear…