Quantum discrete Dubrovin equations

Abstract

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 (Nijhoff F W 2000 Chaos, Solitons and Fractals 11 19-28). The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.

Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations

“…,− = ( − ) 21 ( )∕ 21 0 ( ), which implies (57) by using (33). ■ Lemma 2 gives the total zeros and some poles.…”

“…The latter gave rise to a discrete analog of the Kowalewski‐Dubrovin equations, describing the dynamics in terms of the separation variables. The quantization of the latter systems have been investigated as well in connection with integrable quantum field systems 31–33 . Symplectic mappings related to higher‐order counterparts of the KdV type, eg, the Boussinesq type, have been studied as well 34…”

“…The quantization of the latter systems have been investigated as well in connection with integrable quantum field systems. [31][32][33] Symplectic mappings related to higher-order counterparts of the KdV type, eg, the Boussinesq type, have been studied as well. 34 The motivation for this paper originates from Ref.…”

Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations

“…The latter gave rise to a discrete analogue of the Kowalewski-Dubrovin equations, describing the dynamics in terms of the separation variables. The quantization of the latter systems have been investigated as well in connection with integrable quantum field systems [21][22][23].…”