On the strong DR/DZ equivalence conjecture
Xavier Blot, Danilo Lewanski, Sergey Shadrin
TL;DR
This paper proves the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy, confirming a conjecture linking two integrable systems derived from semi-simple cohomological field theories.
Contribution
It establishes the Miura equivalence of two integrable hierarchies associated with semi-simple cohomological field theories, confirming a longstanding conjecture.
Findings
Proves the Miura equivalence of the two hierarchies
Confirms the conjecture by Buryak and others
Bridges two important integrable systems in mathematical physics
Abstract
We establish the Miura equivalence of two integrable systems associated to a semi-simple cohomological field theory: the double ramification hierarchy of Buryak and the Dubrovin-Zhang hierarchy. This equivalence was conjectured by Buryak and further refined by Buryak, Dubrovin, Gu\'er\'e, and Rossi.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Polynomial and algebraic computation