Dynamics of resonant soliton, novel hybrid interaction, complex N-soliton and the abundant wave solutions to the (2+1)-dimensional Boussinesq equation

Abstract

The presented work concerns with some novel solutions of the (2+1)-dimensional Boussinesq equation (BE), which acts as an important model for shallow water wave. Some resonant soliton solutions such as the X-shape soliton (XSS) and Y-shape soliton (YSS) solutions are developed via imposing the resonant conditions on the N-soliton solutions (N-SSs) that developed by the Hirota bilinear approach(HBA). Based on the XSS and YSS solutions, the novel hybrid interactions including the interaction between the 1-soliton and the YSS, the interaction between two YSS solutions are extracted. In addition, the complex N-SSs are also explored and discussed. Finally, the travelling wave solutions including the bright solitary and kinky solitary wave solutions are studied by employing the Bernoulli sub-equation function method (BSEFM). The graphs of the attained solutions are drawn to show the physical properties. The findings of this study are expected to help us apprehend the dynamics of the (2+1)-dimensional BE better.