In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattices, whose continuum limit is the AKNS hierarchy. In contrast to other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalization. We also solve the associated spectral problem and explicity construct action-angle variables through the r-matrix approach.
Merola, I., Ragnisco, O., Zhang, T.g. (1994). A NOVEL HIERARCHY OF INTEGRABLE LATTICES. INVERSE PROBLEMS, 10(6), 1315-1334 [10.1088/0266-5611/10/6/009].
A NOVEL HIERARCHY OF INTEGRABLE LATTICES
RAGNISCO, Orlando;
1994-01-01
Abstract
In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattices, whose continuum limit is the AKNS hierarchy. In contrast to other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalization. We also solve the associated spectral problem and explicity construct action-angle variables through the r-matrix approach.File in questo prodotto:
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