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Canonicity of Baecklund transformation: r-matrix approach. II

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.

preprint1999arXivOpen access
E. K. Sklyanin
solv-intnlin.SI
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E. K. Sklyanin

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