Bihamiltonian structure of the (n,1)-type rational reductions of the 2D-Toda hierarchy

2026/06/22 by Haonan Qu, Qiulan Zhao · 1 voice · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.DG

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Abstract

We derive a local bihamiltonian structure for the rational reduction of the 2D-Toda hierarchy (RR2T) of (n,1)-type by direct computations, and construct an (n+1)-dimensional semisimple generalized Frobenius manifold with non-flat unity whose Principal Hierarchy contains its dispersionless flows.

Citations

• Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold
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• On Hamiltonian perturbations of hyperbolic systems of conservation laws
• The Hamiltonian structures of the two-dimensional Toda lattice and R-matrices
• The Extended Toda Hierarchy
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Deformations of the KdV hierarchy and related soliton equations
• Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
• Geometry of 2d topological field theories

Cited by

• Tri-Hamiltonian structure of an asymmetric generalized Ablowitz-Ladik hierarchy and a Frobenius manifold

Discussions

• Haonan Qu, Qiulan Zhao: Bihamiltonian structure of the $(n,1)$-type rational reductions of the 2D-Toda hierarchy https://arxiv.org/abs/2606.23167 https://arxiv.org/pdf/2606.23167 https://arxiv.org/htm [bsky, 0 points, 0 comments]

Related

• Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold
• Rational reductions of the 2D-Toda hierarchy and mirror symmetry
• Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies
• Reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations