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) Bäcklund transformation for the oriented associativity equations.

arXiv comment18 pages, LaTeX; two minor typos in Corollary 5 fixed; to appear in J. Phys. A: Math. Theor.;

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Cited by in corpus (4)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries
• Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets
• WDVV equations: Hamiltonian operators and symbolic computations