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A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations

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Abstract

Nonlinear dispersive generalized Benjiamin–Bona–Mahony equations are studied by using a generalized algebraic method. New abundant families of explicit and exact traveling wave solutions, including triangular periodic, solitary wave, periodic-like, soliton-like, rational and exponential solutions are constructed, which are in agreement with the results reported in other literatures, and some new results are obtained. These solutions will be helpful to the further study of the physical meaning and laws of motion of the nature and the realistic models. The proposed method in this paper can be further extended to the 2+1 dimensional and higher dimensional nonlinear evolution equations or systems of equations.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Liang Gao, W. Xu & Y. Tang

  2. Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an, 710049, China

    G. Meng

Authors
  1. Liang Gao
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  2. W. Xu
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  3. Y. Tang
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  4. G. Meng
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Correspondence to Liang Gao.

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Gao, L., Xu, W., Tang, Y. et al. A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations. Nonlinear Dyn 52, 337–345 (2008). https://doi.org/10.1007/s11071-007-9282-6

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  • DOI: https://doi.org/10.1007/s11071-007-9282-6

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