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Integrable differential systems of topological type and reconstruction by the topological recursion

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 نشر من قبل Olivier Marchal
 تاريخ النشر 2016
  مجال البحث فيزياء
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Starting from a $dtimes d$ rational Lax pair system of the form $hbar partial_x Psi= LPsi$ and $hbar partial_t Psi=RPsi$ we prove that, under certain assumptions (genus $0$ spectral curve and additional conditions on $R$ and $L$), the system satisfies the topological type property. A consequence is that the formal $hbar$-WKB expansion of its determinantal correlators, satisfy the topological recursion. This applies in particular to all $(p,q)$ minimal models reductions of the KP hierarchy, or to the six Painleve systems.



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