Exact Poisson pencils, $τ$-structures and topological hierarchies

Gregorio Falqui; Paolo Lorenzoni

doi:10.1016/j.physd.2011.11.009

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arXiv · 1106.1546

Exact Poisson pencils, $τ$-structures and topological hierarchies

Gregorio Falqui·Paolo Lorenzoni

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Abstract

We discuss, in the framework of Dubrovin-Zhang's 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.

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Gregorio Falqui, Paolo Lorenzoni. 2011-12-22. Exact Poisson pencils, $τ$-structures and topological hierarchies. https://doi.org/10.1016/j.physd.2011.11.009

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