We define a new class of solutions to the WDVV associativity equations. This class is selected by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classification of such linearly degenerate solutions of WDVV to a particular case of the so-called algebraic Riccati equation and, in this way we arrive at a complete classification of irreducible solutions.
Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations
Dubrovin, Boris;
2011-01-01
Abstract
We define a new class of solutions to the WDVV associativity equations. This class is selected by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classification of such linearly degenerate solutions of WDVV to a particular case of the so-called algebraic Riccati equation and, in this way we arrive at a complete classification of irreducible solutions.File in questo prodotto:
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