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math-ph2024
Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies
Si-Qi Liu, Haonan Qu, Youjin Zhang
For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Leg…
math-ph2024
The extended Ablowitz-Ladik hierarchy and a generalized Frobenius manifold
Si-Qi Liu, Yuewei Wang, Youjin Zhang
We define a certain extension of the Ablowitz-Ladik hierarchy, and prove that this extended integrable hierarchy coincides with the topological deformation of the Principal Hierarc…
math-ph2024
Solutions of the loop equations of a class of generalized Frobenius manifolds
Si-Qi Liu, Haonan Qu, Yuewei Wang +1
We prove the existence and uniqueness of solution of the loop equation associated with a semisimple generalized Frobenius manifold with non-flat unity, and show, for a particular e…