1,721,031 research outputs found
A q-difference Baxter operator for the Ablowitz-Ladik chain
No full textWe construct the Baxter operator and the corresponding Baxter equation for a quantum version of the Ablowitz-Ladik model. The result is achieved in two different ways: by using the well-known Bethe ansatz technique and by looking at the quantum analogue of the classical Backlund transformations. General results about integrable models governed by the same r-matrix algebra will be given. Baxter's equation comes out to be a q-difference equation involving both the trace and the quantum determinant of the monodromy matrix. The spectrality property of the classical Backlund transformations gives a trace formula representing the classical analogue of Baxter's equation. A q-integral representation of the Baxter operator is discussed
Backlund transformations and Hamiltonian flows
No full textIn this work we show that, under certain conditions, parametric Backlund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given
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