相关论文: A new approach to the Darboux-Backlund transformat…

A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of…

We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the…

In the first part of the paper we present the dressing method which generates multi-soliton solutions to integrable systems of nonlinear partial differential equations. We compare the approach of Neugebauer with that of Zakharov, Shabat and…

We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in…

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its…

A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and…

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…

The application of the Darboux Transformation method to the integrable model of Cylindrically Symmetrical Chiral field has been considered. The associated linear system of matrix equations has been proposed and the properties of symmetrie…

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…

A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of…

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…

Singular Darboux transformations, in contrast to the conventional ones, have a singular matrix as a coefficient before the derivative. We incorporated such transformations into a chain of conventional transformations and presented…

The Darboux process, also known by many other names, played a very important role in some extremely enjoyable joint work that Hans and I did 25 years ago. I revisit a version of this problem in a case when scalars are replaced by matrices,…

Darboux transformation plays a key role in constructing explicit closed-form solutions of completely integrable systems. This paper provides an algebraic construction of generalized Darboux matrices with the same poles for the $2\times2$…

We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Backlund transformation can be viewed as a nonevolutionary integrable differential…

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

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…

We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in…

We review some of the fundamental notions associated to the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary…

In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see…