Abstract
In this paper, a \((3+1)\)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six bilinear equations and involves nine arbitrary parameters. With multiple exponential function method and symbolic computation, nonresonant-typed one-, two-, and three-wave solutions are obtained. Furthermore, two classes of lump solutions to the dimensionally reduced cases with \(y=x\) and \(y=z\) are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.
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Acknowledgements
This work is supported by the Open Fund of IPOC (BUPT) under Grant No. IPOC2016B008. Y. H. Yin is supported by the Project of National Innovation and Entrepreneurship Training Program for College Students under Grant No. 170170007. W. X. Ma is supported in part by the National Natural Science Foundation of China under Grant Nos. 11371326 and 11271008, Natural Science Foundation of Shanghai under Grant No. 11ZR1414100, Zhejiang Innovation Project of China under Grant No. T200905, the First-class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project (No. A13-0101-12-004), and the Distinguished Professorship at Shanghai University of Electric Power.
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Gao, LN., Zi, YY., Yin, YH. et al. Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation. Nonlinear Dyn 89, 2233–2240 (2017). https://doi.org/10.1007/s11071-017-3581-3
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DOI: https://doi.org/10.1007/s11071-017-3581-3