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Bäcklund Transformations for the Degasperis-Procesi Equation

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Abstract

We consider the Bäcklund transformation for the Degasperis-Procesi (DP) equation. Using the reciprocal transformation and the associated DP equation, we construct the Bäcklund transformation for the DP equation involving both dependent and independent variables. We also obtain the corresponding nonlinear superposition, which we use together with the Bäcklund transformation to derive some soliton solutions of the DP equation.

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Acknowledgments

The authors thank Professor Q. P. Liu for the discussions and suggestions. The illuminating remarks of a referee were useful for improving the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanning Normal University, Nanning, China

    Hui Mao

  2. Department of Mathematics, China University of Mining and Technology, Beijing, China

    Gaihua Wang

Authors
  1. Hui Mao
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  2. Gaihua Wang
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Correspondence to Hui Mao.

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Conflicts of interest

The authors declare no conflicts of interest.

This research is supported by the National Natural Science Foundation of China (Grant Nos. 11905110, 11871471, and 11931017), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFBA050020), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Guangxi Zhuang Autonomous Region, China (Grant No. 2019KY0417).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 3, pp. 365–379, June, 2020.

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Mao, H., Wang, G. Bäcklund Transformations for the Degasperis-Procesi Equation. Theor Math Phys 203, 747–760 (2020). https://doi.org/10.1134/S0040577920060045

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