Canonicity of Baecklund transformation: r-matrix approach. I

Details Canonicity of Baecklund transformation: r-matrix approach. I Canonicity of Baecklund transformation: r-matrix approach. I

1999-03-25

arxiv.org/abs/solv-int/9903016v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages, LATEX-2e, macros included

Scientific paper

For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix
(such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a
general procedure for constructing Baecklund transformation is proposed. The
corresponding BT is shown to preserve the Poisson bracket. The proof is given
by a direct calculation using the r-matrix expression for the Poisson bracket.

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