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

B. A. Dubrovin; M. V. Pavlov; S. A. Zykov

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arXiv · 1401.0719

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

B. A. Dubrovin·M. V. Pavlov·S. A. Zykov

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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.

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B. A. Dubrovin, M. V. Pavlov, S. A. Zykov. 2014-01-03. Linearly Degenerate Hamiltonian PDEs and a New Class of Solutions to the WDVV Associativity Equations. https://arxiv.org/abs/1401.0719

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