Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
Artur Sergyeyev
TL;DR
This paper develops infinite hierarchies of nonlocal symmetries for the oriented associativity equations, extending previous work on WDVV equations, and introduces transformations like Darboux and Bäcklund for these equations.
Contribution
It constructs new infinite hierarchies of nonlocal symmetries for the oriented associativity equations using spectral problems, generalizing prior results for WDVV equations.
Findings
Established infinite hierarchies of nonlocal symmetries
Derived Darboux-type and Bäcklund transformations
Extended symmetry structures beyond previous work
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.
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