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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
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
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
Linking options:
https://www.mathnet.ru/eng/faa3053https://doi.org/10.4213/faa3053 https://www.mathnet.ru/eng/faa/v45/i4/p49
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Abstract page: | 670 | Full-text PDF : | 256 | References: | 76 | First page: | 28 |
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