359 research outputs found

### Hydrodynamic reductions and solutions of a universal hierarchy

The diagonal hydrodynamic reductions of a hierarchy of integrable
hydrodynamic chains are explicitly characterized. Their compatibility with
previously introduced reductions of differential type is analyzed and their
associated class of hodograph solutions is discussed.Comment: 19 page

### Elementary Darboux transformations and factorization

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.Comment: 10 page

### The model equation of soliton theory

We consider an hierarchy of integrable 1+2-dimensional equations related to
Lie algebra of the vector fields on the line. The solutions in quadratures are
constructed depending on $n$ arbitrary functions of one argument. The most
interesting result is the simple equation for the generating function of the
hierarchy which defines the dynamics for the negative times and also has
applications to the second order spectral problems. A rather general theory of
integrable 1+1-dimensional equations can be developed by study of polynomial
solutions of this equation under condition of regularity of the corresponding
potentials.Comment: 17

### The Canonical Symmetry for Integrable Systems

The properties of discrete nonlinear symmetries of integrable equations are
investigated. These symmetries are shown to be canonical transformations. On
the basis of the considered examples, it is concluded, that the densities of
the conservation laws are changed under these transformations by spatial
divergencies.Comment: 17 pages, LaTeX, IHEP 92-14

### Dressing chain for the acoustic spectral problem

The iterations are studied of the Darboux transformation for the generalized
Schroedinger operator. The applications to the Dym and Camassa-Holm equations
are considered.Comment: 16 pages, 6 eps figure

### Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra

Boundary value problems for integrable nonlinear partial differential
equations are considered from the symmetry point of view. Families of boundary
conditions compatible with the Harry-Dym, KdV and MKdV equations and the
Volterra chain are discussed. We also discuss the uniqueness of some of these
boundary conditions.Comment: 25 pages , Latex , no figure

### Discrete symmetry's chains and links between integrable equations

The discrete symmetry's dressing chains of the nonlinear Schrodinger equation
(NLS) and Davey-Stewartson equations (DS) are consider. The modified NLS (mNLS)
equation and the modified DS (mDS) equations are obtained. The explicitly
reversible Backlund auto-transformations for the mNLS and mDS equations are
constructed. We demonstrate discrete symmetry's conjugate chains of the KP and
DS models. The two-dimensional generalization of the P4 equation are obtained.Comment: 20 page

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