Equations of Associativity in Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type

Abstract

Equations of associativity in two-dimensional topological field theory (they are known also as the Witten-Dijkgraaf-H.Verlinde-E.Verlinde (WDVV) system) are represented as an example of the general theory of integrable Hamiltonian nondiagonalizable (i.e., do not possessing Riemann invariants) systems of hydrodynamic type. A corresponding local nondegenerate Hamiltonian structure of hydrodynamic type (Poisson bracket of Dubrovin-Novikov type) is found. For n=3 the equations of associativity are reduced to the integrable three wave system by a chain of explicit transformations. Any solution of the integrable three wave system generates solutions of the equations of associativity. Explicit Bäcklund type transformations connecting solutions of different equations of associativity are found.

arXiv comment15 pages, plain tex

Cited by in corpus (5)

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• Towards the classification of homogeneous third-order Hamiltonian operators
• Invariant description of solutions of hydrodynamic type systems in hodograph space: hydrodynamic surfaces
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• Symmetry reductions of a particular set of equations of associativity in twodimensional topological field theory