Solitary, kink and periodic wave solutions of the (3+1)-dimensional Hirota–Satsuma–Ito-like equation

In this article, we consider new solutions to the (3+1)-dimensional Hirota–Satsuma–Ito-like (HSIl) equation by using the exp-function and its expansion methods. This model describes the unidirectional propagation of shallow water waves. The is rewritten as an ordinary differential equation by the traveling wave transformation. Some exact traveling wave solutions of this equation are obtained based on the homogeneous balance method, which includes solitons, kinks, periodic wave solutions, etc. The derived results are innovative and have important applications in the current field of mathematical physics research. To further investigate the properties of these solutions, the dynamical behaviors of these solutions are analyzed. The results show that the scheme is completely powerful and effective.