Linearly Degenerate Hamiltonian PDEs and a New Class of Solutions to the WDVV Associativity Equations

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 cas...

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Bibliographic Details
Published in:arXiv.org 2014-01
Main Authors: Dubrovin, B A, Pavlov, M V, Zykov, S A
Format: Article
Language:English
Subjects:
Associativity
Classification
Mathematical analysis
Riccati equation
Online Access:Get full text
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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.
ISSN:2331-8422