Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

Si-Qi Liu; Zhe Wang; Youjin Zhang

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arXiv · 2305.10851

Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

Si-Qi Liu·Zhe Wang·Youjin Zhang

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Abstract

For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarchy. Moreover, we show that the central invariants of the bihamiltonian structure are preserved under such a linear reciprocal transformation.

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Si-Qi Liu, Zhe Wang, Youjin Zhang. 2023-05-18. Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations. https://arxiv.org/abs/2305.10851

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