Abundant wave solutions for generalized Hietarinta equation with Hirota’s bilinear operator

In this work, we study the generalized ([Formula: see text])-dimensional Hietarinta equation by utilizing Hirota’s bilinear method. In addition, the lump solution and breather solution are presented. Using suitable mathematical assumptions, the new types of lump, singular, and breather soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing equation. Moreover, we give a lot of graphs in some subsections to determine the analysis of behavior solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation. The results are useful for obtaining and explaining some new soliton phenomena.