Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations
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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.
Key wordsFrobenius manifold WDVV associativity equations linearly degenerate PDEs algebraic Riccati equation
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