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The extended Z N -Toda hierarchy

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Abstract

We construct the extended flow equations of a new Z N -Toda hierarchy taking values in a commutative subalgebra Z N of gl(N,C). We give the Hirota bilinear equations and tau function of this new extended Z N -Toda hierarchy. Taking the presence of logarithmic terms into account, we construct some extended vertex operators in generalized Hirota bilinear equations, which might be useful in topological field theory and the Gromov–Witten theory. We present the Darboux transformations and bi-Hamiltonian structure of this hierarchy. Using Hamiltonian tau-symmetry, we obtain another tau function of this hierarchy with some unknown mysterious relation to the tau function derived using the Sato theory.

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Authors and Affiliations

  1. Department of Mathematics and Ningbo Collaborative Innovation Center of Nonlinear Hazard System of Ocean and Atmosphere, Ningbo University, Ningbo, China

    Chuanzhong Li & Jingsong He

Authors
  1. Chuanzhong Li
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  2. Jingsong He
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Correspondence to Chuanzhong Li.

Additional information

Chuanzhong Li is supported by the National Natural Science Foundation of China (Grant Nos. 11201251 and 11571192), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15A010004), and the Natural Science Foundation of Ningbo (Grant Nos. 2015A610157 and 2014A610029).

Jingsong He is supported by the National Natural Science Foundation of China (Grant No. 11271210) and the K. C. Wong Magna Fund in Ningbo University.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 2, pp. 289–312, November, 2015.

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Li, C., He, J. The extended Z N -Toda hierarchy. Theor Math Phys 185, 1614–1635 (2015). https://doi.org/10.1007/s11232-015-0368-x

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  • DOI: https://doi.org/10.1007/s11232-015-0368-x

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