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An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type

Xiang-Ke Chang Xing-Biao Hu Shi-Hao Li Jun-Xiao Zhao

Dynamical Systems mathscidoc:1912.43171

Advances in Mathematics, 338, 1077-1118, 2018.11
The Novikov equation is an integrable analogue of the CamassaHolm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this paper, an approach involving Pfaffians is applied to study multipeakons of the Novikov equation. First, we show that the Novikov peakon ODEs describe an isospectral flow on the manifold cut out by certain Pfaffian identities. Then, a link between the Novikov peakons and the finite Toda lattice of BKP type (B-Toda lattice) is established based on the use of Pfaffians. Finally, certain generalizations of the Novikov equation and the finite B-Toda lattice are proposed together with special solutions. To our knowledge, it is the first time that the peakon problem is interpreted in terms of Pfaffians.
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@inproceedings{xiang-ke2018an,
  title={An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type},
  author={Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li, and Jun-Xiao Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112723206263731},
  booktitle={Advances in Mathematics},
  volume={338},
  pages={1077-1118},
  year={2018},
}
Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li, and Jun-Xiao Zhao. An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type. 2018. Vol. 338. In Advances in Mathematics. pp.1077-1118. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112723206263731.
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