A strange recursion operator demystified

Details A strange recursion operator demystified A strange recursion operator demystified

2004-06-16

arxiv.org/abs/nlin/0406032v2

J.Phys. A38 (2005) L257

Nonlinear Sciences

Exactly Solvable and Integrable Systems

5 pages, LaTeX 2e, a new result added (see the last paragraph of the abstract); the bibliography updated and extended

Scientific paper

10.1088/0305-4470/38/15/L03

We show that a new integrable two-component system of KdV type studied by Karasu (Kalkanli) et al. (arXiv: nlin.SI/0203036) is bihamiltonian, and its recursion operator, which has a highly unusual structure of nonlocal terms, can be written as a ratio of two compatible Hamiltonian operators. Using this, we prove that the system in question possesses an infinite hierarchy of local commuting generalized symmetries and conserved quantities in involution, and the evolution systems corresponding to these symmetries are bihamiltonian as well. We also show that upon introduction of suitable nonlocal variables the nonlocal terms of the recursion operator under study can be written in the usual form, with the integration operator $D^{-1}$ appearing in each term at most once.

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