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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 4, Pages 49–64
DOI: https://doi.org/10.4213/faa3053 (Mi faa3053) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
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DOI: https://doi.org/10.4213/faa3053
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.
Received: 30.05.2011
English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 4, Pages 278–290
DOI: https://doi.org/10.1007/s10688-011-0030-9
Bibliographic databases:
Document Type: Article
UDC: 917.95
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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