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Soliton solutions and Bäcklund transformations of a (2 + 1)-dimensional nonlinear evolution equation via the Jaulent–Miodek hierarchy

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Abstract

In this paper, a (2 + 1)-dimensional nonlinear evolution equation generated via the Jaulent–Miodek hierarchy is investigated. Based on the Bell polynomials and Hirota method, bilinear forms and Bäcklund transformations are derived. One- and two-soliton solutions are constructed via symbolic computation. Soliton solutions are obtained through the Bäcklund transformations. We can get three types by choosing different parameters: the kink, bell-shape, and anti-bell-shape solitons. Propagation of the one soliton and elastic interactions between the two solitons are discussed graphically. After the interaction of the two bell-shape or anti-bell-shape solitons, solitonic shapes and amplitudes keep invariant except for some phase shifts, while after the interaction of the kink soliton and anti-bell-shape soliton, the anti-bell-shape soliton turns into a bell-shape one, and the kink soliton keeps its shape, with their amplitudes unchanged.

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Acknowledgments

This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023, by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) under Grant No. IPOC2013B008, and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing , 100876, China

    De-Yin Liu, Bo Tian, Yan Jiang & Wen-Rong Sun

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  1. De-Yin Liu
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  2. Bo Tian
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  3. Yan Jiang
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  4. Wen-Rong Sun
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Correspondence to Bo Tian.

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Liu, DY., Tian, B., Jiang, Y. et al. Soliton solutions and Bäcklund transformations of a (2 + 1)-dimensional nonlinear evolution equation via the Jaulent–Miodek hierarchy. Nonlinear Dyn 78, 2341–2347 (2014). https://doi.org/10.1007/s11071-014-1581-0

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  • DOI: https://doi.org/10.1007/s11071-014-1581-0

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