The Calogero--Bogoyavlenskii--Schiff breaking soliton equation: recursion operators and higher symmetries

Abstract

We find two one-parametric families of recursion operators and use them to construct higher symmetries for the Calogero--Bogoyavlenskii--Schiff breaking soliton equation. Then we prove that the recursion operators from the first family pair-wise commute with respect to the Nijenhuis bracket (are compatible).