Functional Analysis and Its Applications

, Volume 45, Issue 4, pp 278–290 | Cite as

Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations

  • B. A. DubrovinEmail author
  • M. V. Pavlov
  • S. A. Zykov


We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.

Key words

Frobenius manifold WDVV associativity equations linearly degenerate PDEs algebraic Riccati equation 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • B. A. Dubrovin
    • 1
    • 2
    Email author
  • M. V. Pavlov
    • 3
  • S. A. Zykov
    • 4
    • 5
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Laboratory of Geometric methods in Mathematical Physics V. A. Steklov Mathematical InstituteMoscow State UniversityMoscowRussia
  3. 3.Laboratory of Geometric methods in Mathematical Physics P. N. Lebedev Physical Institute of RASMoscow State UniversityMoscowRussia
  4. 4.University of SalentoLecceItaly
  5. 5.Department of PhysicsInstitute of Metal Physics, Ural branch of RASEkaterinburgRussia

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