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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 4, Pages 49–64 (Mi faa3053)  

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

B. A. Dubrovinabc, S. A. Zykovde, M. V. Pavlovfc

a Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
b V. A. Steklov Mathematical Institute
c Laboratory of Geometric methods in Mathematical Physics, Moscow State University, Moscow, Russia
d Institute of Metal Physics, Ural branch of RAS, Ekaterinburg, Russia
e University of Salento, Lecce, Italy
f P. N. Lebedev Physical Institute of RAS, Moscow

Abstract: 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.

Keywords: Frobenius manifold, WDVV associativity equations, linearly degenerate PDEs, algebraic Riccati equation.

DOI: https://doi.org/10.4213/faa3053

Full text: PDF file (235 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:4, 278–290

Bibliographic databases:

UDC: 917.95
Received: 30.05.2011

Citation: B. A. Dubrovin, S. A. Zykov, M. V. Pavlov, “Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 49–64; Funct. Anal. Appl., 45:4 (2011), 278–290

Citation in format AMSBIB
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\paper Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations
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