Geodesic
Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 49-64

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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
Mots-clés : algebraic Riccati equation. 
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     author = {B. A. Dubrovin and S. A. Zykov and M. V. Pavlov},
     title = {Linearly degenerate {Hamiltonian} {PDEs} and a new class of solutions to the {WDVV} associativity equations},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {49--64},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a4/}
}
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B. A. Dubrovin; S. A. Zykov; M. V. Pavlov. Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 49-64. http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a4/