Integrable Systems of Double Ramification Type

@article{Buryak2016IntegrableSO,
  title={Integrable Systems of Double Ramification Type},
  author={Alexandr Buryak and Boris Dubrovin and J'er'emy Gu'er'e and Paolo Rossi},
  journal={International Mathematics Research Notices},
  year={2016}
}
In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable hierarchies and prove that the quantum DR hierarchy enjoys this property. We determine explicitly the genus $1$ quantum correction and, as an application, compute completely the quantization of the $3$- and $4$-KdV hierarchies (the DR hierarchies for Witten’s $3$- and $4$-spin theories). We then focus… 

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