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Frobenius manifolds and integrable hierarchies of the topological type

Abstract:

Frobenius manifolds naturally arise in the deformation theory of integrable PDEs. An important class of hierarchies of integrable PDEs is canonically associated with an arbitrary semisimple Frobenius manifold. The Tau-function of a particular solution to such a hierarchy conjecturally satisfies all universal identities arising in the theory of Gromov-Witten invariants and their descendants. It looks like the very same integrable PDEs can be used in the asymptotic theory of nonlinear oscillatory waves.