Abstract
The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of the circle. A new two-parametric hierarchy of commuting to each other Monge type Hamiltonian vector fields is constructed. This hierarchy, jointly with a specially constructed reciprocal transformation, produces a Frobenius manifold potential function in terms of solutions of these Monge type Hamiltonian systems.
Highlights
The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations
Let us start with an interesting mathematical structure, suggested in [1,2,3,4,5], on the space of smooth functions: consider a real-valued C ∞ -smooth differentiable Frobenius manifold potential function F ∈ C ∞ (Rn ; R) and denote their partial derivatives as Academic Editors: Pilar Garcia
Let F : M → R be a potential function on the Frobenius manifold M, defined by means of the set of asymptotic relationship
Summary
The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. We succeeded in describing a class of Frobenius manifold structures, generated by the non-linear Monge type evolution systems (13) and (14).
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