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arXiv · 2411.15496

Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies

Si-Qi Liu·Haonan Qu·Youjin Zhang
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Abstract

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 Legendre-extended Principal Hierarchies, are related by a certain linear reciprocal transformation; we also show, under the semisimplicity condition, that the topological deformations of these Legendre-extended Principal Hierarchies are related by the same linear reciprocal transformation.

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Si-Qi Liu, Haonan Qu, Youjin Zhang. 2024-11-23. Legendre transformations of a class of generalized Frobenius manifolds and the associated integrable hierarchies. https://arxiv.org/abs/2411.15496

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