https://doi.org/10.1140/epjp/s13360-020-00729-6
Regular Article
Exact solution of Boussinesq equations for propagation of nonlinear waves
Institute of Computational Modeling, SB RAS, Krasnoyarsk, Russia
Received:
22
May
2020
Accepted:
28
August
2020
Published online:
14
September
2020
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.
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).
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
