By means of the Hirota bilinear method, lump-type solution and two types of interaction solutions of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation are obtained, respectively. Lump-type solution is constructed by assuming f in the corresponding bilinear equation as a ternary quadratic polynomial function. It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of stripe solitons, and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton. The corresponding phenomena are vividly demonstrated by the graphs.

In this paper, the lump-type solutions, interaction solutions, and periodic lump solutions of the generalized ([Formula: see text])-dimensional Burgers equation were obtained by using the ansatz method. Based on a variable transformation, the generalized ([Formula: see text])-dimensional Burgers equation was transformed into a bilinear equation. And then, lump-type solutions, two kinds of interaction solutions, and periodic lump solutions were obtained via solutions of the bilinear equation. Fission and fusion phenomena are found in the process of interaction between lump-type soliton and one stripe soliton, which can derive the lumpoff wave solution. The dynamic characteristics of these solutions were vividly displayed by graphics.