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

TitleLinearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations
Publication TypeJournal Article
Year of Publication2011
AuthorsDubrovin, B, Pavlov, MV, Zykov, SA
JournalFunctional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290
KeywordsFrobenius manifold
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.

URLhttp://hdl.handle.net/1963/6430
DOI10.1007/s10688-011-0030-9

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