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Obtaining multisoliton solutions of the (2+1)-dimensional Camassa–Holm system using Darboux transformations

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Abstract

We construct and study Darboux transformations for the \((2{+}1)\)-dimensional Camassa–Holm system. We apply a reciprocal transformation that relates the \((2{+}1)\)-dimensional Camassa–Holm system and the linear system associated with the modified Kadomtsev–Petviashvili hierarchy. Using three Darboux transformation operators, we obtain three types of solutions for the \((2{+}1)\)-dimensional Camassa–Holm system, of which one is a multisoliton solution. In addition, we briefly discuss rational solutions.

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Funding

This research is supported by the National Natural Science Foundation of China (Grant Nos. 11905110 and 11871471), 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).

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

    Hui Mao

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  1. Hui Mao
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Correspondence to Hui Mao.

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Mao, H. Obtaining multisoliton solutions of the (2+1)-dimensional Camassa–Holm system using Darboux transformations. Theor Math Phys 205, 1638–1651 (2020). https://doi.org/10.1134/S0040577920120065

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