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Kernel formula approach to the universal Whitham hierarchy

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Abstract

Based on the kernel formula proposed by Carroll and Kodama, we derive the dispersionless Hirota equations of the universal Whitham hierarchy. We also verify the associativity equations in this hierarchy from the dispersionless Hirota equations and give a realization of the associative algebra with the structure constants expressed in terms of residue formulas.

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Authors and Affiliations

  1. Department of Mechanical Engineering, WuFeng Institute of Technology, Chiayi, Taiwan

    Hsin-Fu Shen

  2. General Education Center, National Chinyi University of Technology, Taichung, Taiwan

    Niann-Chern Lee

  3. Department of Physics, National Chung Cheng University, Chiayi, Taiwan

    Ming-Hsien Tu

Authors
  1. Hsin-Fu Shen
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  2. Niann-Chern Lee
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  3. Ming-Hsien Tu
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Corresponding author

Correspondence to Ming-Hsien Tu.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 165, No. 2, pp. 257–271, November, 2010.

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Shen, HF., Lee, NC. & Tu, MH. Kernel formula approach to the universal Whitham hierarchy. Theor Math Phys 165, 1456–1469 (2010). https://doi.org/10.1007/s11232-010-0121-4

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  • DOI: https://doi.org/10.1007/s11232-010-0121-4

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