Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2000-12-07
Proc. Sem. Diff. Geom. (Opava, 2000), D. Krupka ed., Math. Publ., vol.2 (Silesian Univ. in Opava, Opava, 2000), p.159--173.
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages, LaTeX; some minor misprints corrected and Appendices A and B slightly rewritten
Scientific paper
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian coverings over these systems. The extended recursion operators are shown to leave this space invariant. These results apply, in particular, to the recursion operators of the majority of known today (1+1)-dimensional integrable evolution systems. We also present some related results and describe the extension of them and of the above results to (1+1)-dimensional systems of PDEs transformable into the evolutionary form. Some examples and applications are given.
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