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Exact Poisson pencils, \(\tau \)-structures and topological hierarchies.(English)Zbl 1318.53102

Summary: We discuss, in the framework of the Dubrovin-Zhang perturbative approach to integrable evolutionary PDEs in \(1+1\) dimensions, the role of a special class of Poisson pencils, called exact Poisson pencils. In particular we show that, in the semisimple case, exactness of the pencil is equivalent to the constancy of the so-called “central invariants” of the theory that were introduced by Dubrovin, Liu and Zhang.

MSC:

53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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