The solitary wave, rogue wave and periodic solutions for the ( $$3+1$$ 3 + 1 )-dimensional soliton equation

Based on the Hirota’s bilinear form, the (\(3+1\))-dimensional soliton equation is investigated. The solitary wave, rogue wave and periodic solutions are obtained. Their interaction behaviors are shown in some three-dimensional plots and corresponding contour plots by setting different values of the parameters.