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

2023/10/16 by Alexandr Buryak, Buryak, Alexandr, Mikhail Troshkin +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2310.10150

openalex publication_date 2023/10/16 · openalex created_date 2023/10/20 · openalex updated_date 2026/07/28

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.

Related

• Hamiltonian Structures and Reciprocal Transformations for the r-KdV-CH Hierarchy
• Reciprocal transformations and deformations of integrable hierarchies
• On the strong DR/DZ equivalence conjecture
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
• Deformations of the Riemann hierarchy and the geometry of M_g,n