Moscow Mathematical Journal

Volume 24, Issue 4, October–December 2024 pp. 513–527.

An Application of the Nonlinear Reciprocal Transformations in the Theory of DR Hierarchies

Authors: Alexandr Buryak (1) and Mikhail Troshkin (2)
Author institution:(1) Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, Moscow, 119048, Russian Federation;
Igor Krichever Center for Advanced Studies, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russian Federation
(2) Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, Moscow, 119048, Russian Federation

Summary:

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.

2020 Math. Subj. Class. 14H10, 37K10.

Keywords: Riemann surface, quantum integrable system, moduli space.

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