%0 Journal Article %J Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 %D 2011 %T Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations %A Boris Dubrovin %A M.V. Pavlov %A Sergei A. Zykov %K Frobenius manifold %X 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 Functional Analysis and Its Applications. Volume 45, Issue 4, December 2011, Pages 278-290 %I Springer %G en %U http://hdl.handle.net/1963/6430 %1 6367 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T11:15:30Z No. of bitstreams: 1 dubrovin_linearly.pdf: 298813 bytes, checksum: 568feaa543b4082cc8e8fab4643dce71 (MD5) %R 10.1007/s10688-011-0030-9