相关论文: Generalized Algebraic Bargmann - Darboux Transform…
Darboux transformation of a second-order linear differential operator is a well-known technique with many applications in mathematics and physics. We study Darboux transformation from the point of view of Markov semigroups of diffusion…
A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.
We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of B\"acklund transformations. These transformations…
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…
We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate…
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 obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and…
Gauge transformation properties for an associated linear system of model Ishimori's magnet model have been discussed. Explicit formulas for the gauge transformation matrix have been obtained. Darboux Transformation has been suggested and…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
For a generalized super KdV equation, three Darboux transformations and the corresponding B\"acklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax…
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux…
We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial \psi}{\partial t}=\sum_{k=1}^r H_k(t)\frac{\partial \psi}{\partial \zeta_k}\,$ $( H_k(t)=…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
Darboux transformations for polynomial perturbations of a real multivariate measure are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate orthogonal polynomials are expressed in terms of last…
Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the…
Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical…
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…
We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund…
We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants. Further, the parabolic, soliton and breather solutions of the GI equation are given as…
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…