Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-03-18
Acta Appl. Math. 83 (2004), no. 1-2, 95--109.
Nonlinear Sciences
Exactly Solvable and Integrable Systems
11 pages, LaTeX 2e, submitted to Acta Appl. Math
Scientific paper
10.1023/B:ACAP.0000035591.77558.
Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild assumptions it allows to bypass the cumbersome check of hereditariness of the recursion operator in question, what is particularly useful for the study of symmetries of newly discovered integrable systems. What is more, unlike the earlier work, the homogeneity of recursion operators and symmetries under a scaling is not assumed as well. An example of nonhereditary recursion operator generating a hierarchy of local symmetries is presented.
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