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Nonlocal symmetries and explicit solutions of the Boussinesq equation

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Abstract

The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlevé equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Xiangpeng Xin, Junchao Chen & Yong Chen

Authors
  1. Xiangpeng Xin
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  2. Junchao Chen
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  3. Yong Chen
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Corresponding author

Correspondence to Xiangpeng Xin.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11275072, 11435005), the Research Fund for the Doctoral Program of Higher Education of China (No. 20120076110024), the Innovative Research Team Program of the National Natural Science Foundation of China (No. 61321064), the Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213), the Shanghai Minhang District Talents of High Level Scientific Research Project and the Talent Fund and K. C. Wong Magna Fund in Ningbo University.

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Xin, X., Chen, J. & Chen, Y. Nonlocal symmetries and explicit solutions of the Boussinesq equation. Chin. Ann. Math. Ser. B 35, 841–856 (2014). https://doi.org/10.1007/s11401-014-0868-2

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  • DOI: https://doi.org/10.1007/s11401-014-0868-2

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