https://doi.org/10.1140/epjp/s13360-023-04521-0
Regular Article
Soliton molecules and other diverse wave solutions of the (2 + 1)-dimensional Boussinesq equation for the shallow water
School of Physics and Electronic Information Engineering, Henan Polytechnic University, 454003, Jiaozuo, China
Received:
11
July
2023
Accepted:
25
September
2023
Published online:
7
October
2023
In the current study, we are mainly concerned with the (2 + 1)-dimensional Boussinesq equation (BE) that plays a major role in describing the shallow water. Firstly, the resonance conditions of the soliton molecules are explored based on the N-soliton solution that extracted via the Hirota bilinear method. Secondly, some new kinds of the different waves solutions including the bright solitary, dark solitary, bright-singular solitary, dark-singular solitary and singular periodic wave solutions are investigated by manipulating two effective methods namely, Wang’s direct mapping method-II(WDMM-II) and Sub-equation method (SEM). The dynamical behaviors of the soliton molecules on the planes such as the 
, 
and 
as well as the other wave solutions are discussed by displaying some graphics. The methods adopted in this work are hopeful to give some new inspiration on the study of the other PDEs in physics.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
