@article {2011, title = {Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations}, journal = {Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290}, year = {2011}, publisher = {Springer}, 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.}, keywords = {Frobenius manifold}, doi = {10.1007/s10688-011-0030-9}, url = {http://hdl.handle.net/1963/6430}, author = {Boris Dubrovin and M.V. Pavlov and Sergei A. Zykov} }