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Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

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Abstract

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China

    Si-Qi Liu & Youjin Zhang

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  1. Si-Qi Liu
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  2. Youjin Zhang
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Correspondence to Youjin Zhang.

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Communicated by Y. Kawahigashi

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Liu, SQ., Zhang, Y. Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case. Commun. Math. Phys. 324, 897–935 (2013). https://doi.org/10.1007/s00220-013-1822-y

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