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Multiple residual symmetries and soliton-cnoidal wave interaction solution of the \((2+1)\)-dimensional negative-order modified Calogero–Bogoyavlenskii–Schiff equation

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Abstract

The residual symmetry for the \((2+1)\)-dimensional negative-order modified Calogero–Bogoyavlenskii–Schiff (nmCBS) equation is derived from the truncated Painlevé expansion, and is extended to the multiple residual symmetries, which can be transformed to Lie point symmetries by introducing a suitable prolonged system. The nth Bäcklund transformation (BT) related to multiple residual symmetries is given in terms of determinant. More importantly, we obtain the explicit soliton-cnoidal wave interaction solution from a consistent differential equation.

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Acknowledgements

This work is supported by the Scientific Research Foundation of Educational Committee of Yunnan Province (no. 2019J0735), and the Construction Plan of Key Laboratory of Institutions of Higher Education of Yunnan Province. D.Q. Qiu acknowledges sincerely Prof. Q.P. Liu for many useful discussions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Wenguang Cheng & Tianzhou Xu

  2. Department of Mathematics, Yuxi Normal University, Yuxi, 653100, People’s Republic of China

    Wenguang Cheng

  3. Department of Mathematics, China University of Mining and Technology, Beijing, 100083, People’s Republic of China

    Deqin Qiu

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  1. Wenguang Cheng
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  2. Deqin Qiu
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  3. Tianzhou Xu
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Correspondence to Deqin Qiu.

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This project was supported by the Scientific Research Foundation of Educational Committee of Yunnan Province (no. 2019J0735), and the Construction Plan of Key Laboratory of Institutions of Higher Education of Yunnan Province.

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Cheng, W., Qiu, D. & Xu, T. Multiple residual symmetries and soliton-cnoidal wave interaction solution of the \((2+1)\)-dimensional negative-order modified Calogero–Bogoyavlenskii–Schiff equation. Eur. Phys. J. Plus 135, 15 (2020). https://doi.org/10.1140/epjp/s13360-019-00035-w

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