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Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations. (English. Russian original) Zbl 1271.37044

Funct. Anal. Appl. 45, No. 4, 278-290 (2011); translation from Funkts. Anal. Prilozh. 45, No. 4, 49-64 (2011).
Summary: 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.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:

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