相关论文: Darboux-type transformations and hyperelliptic cur…
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the…
Additional reductions in the modified k-constrained KP hierarchy are proposed. As a result we obtain generalizations of Kaup-Broer system, Korteweg-de Vries equation and a modification of Korteweg-de Vries equation that belongs to modified…
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that…
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all…
The matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second…
In this paper, we take into account the opinion of involute-evolute curves which lie on fully surfaces and by taking into account the Darboux frames of them we illustrate these curves as special involute-evolute partner D-curves in E3.…
We generalized the mKdV equation in order that the static equations include ${\rm sn}$ differential equation. As a result, a good correspondence was obtained between the KdV equation and the mKdV equation.For general genus two hyperelliptic…
Vertex operators, which are disguised Darboux maps, transform solutions of the KP equation into new ones. In this paper, we show that the bi-infinite sequence obtained by Darboux transforming an arbitrary KP solution recursively forward and…
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…
We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation.…
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…
We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of…
We study additional non-isospectral symmetries of constrained (reduced) N=2 supersymmetric KP hierarchies of integrable ``soliton''-like evolution equations. These symmetries are shown to form an infinite-dimensional non-Abelian superloop…
We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which turns out to be canonical. We also…
We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular…
The Darboux transformations of Krawtchouk polynomials are investigated and all possible exceptional Krawtchouk polynomials obtainable from a single-step Darboux transformation are considered. The properties of these exceptional Krawtchouk…
In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensive list of integrable differential-difference equations…
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…
We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$-…
The matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second…