Canonicity of Baecklund transformation: r-matrix approach. II

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

1999-03-25

arxiv.org/abs/solv-int/9903017v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages, LATEX 2e, macros included

Scientific paper

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.

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