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Multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit: Darboux transformation approach

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Abstract

We propose a new approach for calculating multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit by combining a reciprocal transformation with the Darboux transformation of the negative flow of the Kaup–Kupershmidt hierarchy. In particular, different specifications of the soliton parameters lead to two different types of soliton solutions of the Degasperis–Procesi equation.

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Acknowledgments. The authors are grateful to the referee for the helpful comments. They also thank Professor Q. P. Liu for the useful suggestions and discussions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, China

    Nianhua Li

  2. Department of Mathematics, National Research University “Higher School of Economics,”, Moscow, Russia

    Nianhua Li

  3. Department of Mathematics, School of Science, China University of Mining and Technology, Beijing, China

    Gaihua Wang

  4. School of Science, Zhongyuan University of Technology, Zhengzhou, China

    Yonghui Kuang

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  1. Nianhua Li
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  2. Gaihua Wang
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  3. Yonghui Kuang
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Correspondence to Nianhua Li.

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Conflicts of interest. The authors declare no conflicts of interest.

Additional information

This research is supported in part by the National Natural Science Foundation of China (Grant Nos. 11505064, 11805071, and 11871471) and the Natural Science Foundation of Fujian Province, China (Grant No. 2016J05008).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 2, pp. 205–219, May, 2020.

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Li, N., Wang, G. & Kuang, Y. Multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit: Darboux transformation approach. Theor Math Phys 203, 608–620 (2020). https://doi.org/10.1134/S0040577920050049

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  • DOI: https://doi.org/10.1134/S0040577920050049

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