Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures

Abstract

Combining the construction of integrable systems of hydrodynamic type starting from the Frölicher-Nijenhuis bicomplex $(d,d_L)$ associated with a (1,1)-tensor field $L$ with vanishing Nijenhuis torsion with the construction of flat structures starting from integrable systems of hydrodynamic type we define multi-parameter families of bi-flat structures $(\nabla ,e,\circ ,{\nabla }^{\ast },\ast ,E)$ associated with Frölicher-Nijenhuis bicomplexes. We call these structures Lauricella bi-flat structures since in the n-dimensional semisimple case (n-1) flat coordinates of r are Lauricella functions.

References in corpus (12)

• Integrable hydrodynamic chains
• Flat Structure on the Space of Isomonodromic Deformations
• Complex reflection groups, logarithmic connections and bi-flat F-manifolds
• From Darboux-Egorov system to bi-flat $F$-manifolds
• $F$-manifolds, multi-flat structures and Painlevé transcendents
• $F$-manifolds with eventual identities, bidifferential calculus and twisted Lenard-Magri chains
• Confluence of hypergeometric functions and integrable hydrodynamic type systems
• Natural connections for semi-Hamiltonian systems: The case of the $\epsilon$-system
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Darboux-Egorov system, bi-flat $F$-manifolds and Painlevé VI
• Flat bidifferential ideals and semihamiltonian PDEs
• Regular non-semisimple Dubrovin-Frobenius manifolds

Cited by in corpus (1)

• Regular F -manifolds with eventual identities