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Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

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Abstract.

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China

    Zhonglong Zhao & Bo Han

  2. Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, Canada

    Zhonglong Zhao

Authors
  1. Zhonglong Zhao
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  2. Bo Han
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Correspondence to Zhonglong Zhao.

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Zhao, Z., Han, B. Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation. Eur. Phys. J. Plus 133, 144 (2018). https://doi.org/10.1140/epjp/i2018-11990-3

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  • DOI: https://doi.org/10.1140/epjp/i2018-11990-3

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