(Non)Locality of symmetries and Poisson structures generated using hereditary recursion operators and proof of the Novikov-Maltsev conjecture
Abstract:
For a large class of hereditary recursion operators (ROs), including
overwhelming majority of ROs of (1+1)-dimensional integrable systems known
today, we present new easily verifiable sufficient conditions of locality
of symmetries generated by these ROs. Note that unlike the earlier work
of Sanders and Wang, we do not assume homogeneity and time-independence
of coefficients of ROs in question. Using the above result we prove, under
fairly mild assumptions, the recent conjecture of S.P. Novikov and A.Ya.
Maltsev on the structure of nonlocal terms of higher Poisson structures
generated by the hereditary ROs.