Quantum discrete Dubrovin equations

Details Quantum discrete Dubrovin equations Quantum discrete Dubrovin equations

2004-06-18

arxiv.org/abs/nlin/0406040v1

J. Phys. A: Math. Gen. 37 (2004) 8065--8087

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages

Scientific paper

10.1088/0305-4470/37/33/007

The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the lattice at a constant time-level) evolutions are considered. In the classical limit, the temporal equations reduce to the (classical) discrete Dubrovin equations as given in a previous publication. The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.

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