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Exact solution of Boussinesq equations for propagation of nonlinear waves

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Abstract

In this paper, we consider two Boussinesq models that describe propagation of small-amplitude long water waves. Exact solutions of the classical Boussinesq equation that represent the interaction of wave packets and waves on solitons are found. We use the Hirota representation and computer algebra methods. Moreover, we find various solutions for one of the variants of the Boussinesq system. In particular, these solutions can be interpreted as the fusion and decay of solitary waves, as well as the interaction of more complex structures.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: We do not have any data in repository. All data is available in the article.]

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Authors and Affiliations

  1. Institute of Computational Modeling, SB RAS, Krasnoyarsk, Russia

    O. V. Kaptsov & D. O. Kaptsov

Authors
  1. O. V. Kaptsov
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  2. D. O. Kaptsov
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Correspondence to O. V. Kaptsov.

Additional information

O. V. Kaptsov: This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2020-1631).

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Kaptsov, O.V., Kaptsov, D.O. Exact solution of Boussinesq equations for propagation of nonlinear waves. Eur. Phys. J. Plus 135, 723 (2020). https://doi.org/10.1140/epjp/s13360-020-00729-6

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00729-6

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