Integrable hierarchies associated to infinite families of Frobenius manifolds

Alexey Basalaev, Petr Dunin-Barkowski, Sergey Natanzon

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to A N , D N and B N singularities. In the case of A N Frobenius manifolds our hierarchy turns out to coincide with the dispersionless KP hierarchy; for B N Frobenius manifolds it coincides with the dispersionless BKP hierarchy; and for D N hierarchy it is a certain reduction of the dispersionless 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of A N , D N and B N Frobenius potentials.

Original languageEnglish
Article number115201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number11
Publication statusPublished - 19 Mar 2021


  • Frobenius manifolds
  • integrable hierarchies
  • KP hierarchy
  • singularity theory
  • WDVV equation


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