Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · solv-int/9903017

Canonicity of Baecklund transformation: r-matrix approach. II

E. K. Sklyanin
View original source ↗Read source document ↗Export metadata ↓

Abstract

This is the second part of the paper devoted to the general proof of canonicity of Baecklund transformation (BT) for a Hamiltonian integrable system governed by SL(2)-invariant r-matrix. Introducing an extended phase space from which the original one is obtained by imposing a 1st kind constraint, we are able to prove the canonicity of BT in a new way. The new proof allows to explain naturally the fact why the gauge transformation matrix M associated to the BT has the same structure as the Lax operator L. The technique is illustrated on the example of the DST chain.

Explore related subjects

solv-intnlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E. K. Sklyanin. 1999-03-25. Canonicity of Baecklund transformation: r-matrix approach. II. https://arxiv.org/abs/solv-int/9903017

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2017

The averaging of non-local Hamiltonian structures in Whitham's method

We consider the $m$-phase Whitham's averaging method and propose a procedure of "averaging" of non-local Hamiltonian structures. The procedure is based on the existence of a sufficient number of local commuting integrals of a system and gives a Poisson bracket of Ferapontov type for the Whitham's system. The method can be considered as a generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets.

solv-int↗
arXiv2013

On two aspects of the Painleve analysis

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Backlund transformation related to the Lax pair.

solv-int↗
arXiv2009

The tetrahedral analog of Veneziano amplitude

In solv-int/9812016 it was shown that the Veneziano amplitude in string theory comes naturally from one of the simplest solutions of the functional pentagon equation (FPE). More generally, FPE is intimately connected with the duality condition for scattering processes. Here I find the amplitude that comes the same way from a solution of the functional tetrahedron equation, with the duality replaced by the local Yang - Baxter equation.

solv-int↗