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 case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions. 
B.A. Dubrovin, M.V. Pavlov, S.A. Zykov
nlin.SI