Abstract
The current study aims to develop some novel wave solutions of the (3+1)-dimensional shallow water wave equation (SWWE). First, the Y-type soliton (YTS) solutions are developed via imposing the certain resonant condition to the N-solitons solutions (NSSs) that extracted by the Hirota bilinear approach. Then, the symbolic computation and ansatz function scheme are employed to explore the interaction wave solutions. Eventually, the sub-equation approach is utilized to find the diverse wave solutions which include the kink wave, singular wave and the singular periodic wave solutions. The dynamics of the obtained solutions are presented graphically for revealing the nonlinear physical characteristics. The investigative solutions in this article have not been probed elsewhere and can help us comprehend the nonlinear behaviors of the (3+1)-dimensional SWWE better.
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