Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
Boris Dubrovin, Si-Qi Liu, Youjin Zhang
TL;DR
This paper computes the complete set of invariants for bihamiltonian structures derived from the Drinfeld-Sokolov construction, linking affine Lie algebras to integrable systems and their symmetries.
Contribution
It provides the first explicit calculation of invariants for these bihamiltonian structures, enhancing understanding of their classification and symmetry properties.
Findings
Complete set of invariants computed for bihamiltonian structures
Clarifies the role of Miura type transformations in classifying these structures
Links affine Lie algebras to integrable hierarchies through invariants
Abstract
The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology