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Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

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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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Acknowledgements

This work is supported by NSFC No. 12171268 and No. 12061131014.

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Author notes

  1. S.-Q. Liu, Z. Wang and Y. Zhang have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Si-Qi Liu & Youjin Zhang

  2. Division of Mathematics and Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Zhe Wang

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  1. Si-Qi Liu
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  2. Zhe Wang
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  3. Youjin Zhang
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Correspondence to Youjin Zhang.

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Communicated by Y. Kawahigashi.

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Liu, SQ., Wang, Z. & Zhang, Y. Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations. Commun. Math. Phys. 403, 1109–1152 (2023). https://doi.org/10.1007/s00220-023-04817-3

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