An application of the nonlinear reciprocal transformations in the theory of dr hierarchies

Alexandr Buryak^ab, Mikhail Troshkin<sup>a

a</sup> Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, Moscow, 119048, Russian Federation
^b Igor Krichever Center for Advanced Studies, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russian Federation

Abstract: We prove that the DR hierarchy corresponding to the family of F-cohomological field theories without unit considered in a previous work of the first author together with D. Gubarevich can be “trivialized”, i.e., reduced to two copies of the KdV hierarchy, using a simple nonlinear reciprocal transformation. This gives the first manifestation of a role of nonlinear reciprocal transformation in the theory of integrable systems associated to the moduli spaces of stable curves, beyond the dispersionless limit.

Key words and phrases: riemann surface, quantum integrable system, moduli space.

MSC: 14H10, 37K10

Language: English

DOI: 10.17323/1609-4514-2024-24-4-513-527