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New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada–Kotera model

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Abstract

In this paper, the (2+1)-dimensional Sawada–Kotera model is studied with the Hirota bilinear method, gauge transformation and symbolic computation. Based on an alternative bilinear representation of the model, a bilinear Bäcklund transformation (BT) with three arbitrary constants is derived. Via applying a gauge transformation to this BT and choosing suitable constant parameters, three other sets of bilinear BTs are constructed, among which, the last set is treated as a new bilinear BT and denoted as BTIV hereby. Finally, by performing the perturbation technique on the new bilinear BT, namely BTIV, multisoliton solutions are iteratively achieved, and as an example, the one-, two- and three-soliton solutions are explicitly given. Note that formulas of the soliton solutions obtained hereby through solving the BTIV are different from the previous ones in other literature.

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Acknowledgements

X.L. expresses his sincere thanks to Prof. X.B. Hu for his enthusiastic help and valuable discussions. This work is supported the National Natural Science Foundation of China under Grant No. 61308018, by China Postdoctoral Science Foundation under Grant No. 2012M520154, by the Fundamental Research Funds for the Central Universities (2013JBM088), and partially by the Project of State Key Laboratory of Rail Traffic Control and Safety (No. RCS2012ZT004), Beijing Jiao Tong University.

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  1. Department of Mathematics, Beijing Jiao Tong University, Beijing, 100044, P.R. China

    Xing Lü

  2. State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao Tong University, Beijing, 100044, China

    Xing Lü

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Lü, X. New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada–Kotera model. Nonlinear Dyn 76, 161–168 (2014). https://doi.org/10.1007/s11071-013-1118-y

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