Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations

Abstract

We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen, Kontsevich and Schwarz (arXiv:hep-th/0508221) for the WDVV equations. As a byproduct, we obtain a Darboux-type transformation and a (conditional) B\"acklund transformation for the oriented associativity equations.