The consistent tanh expansion (CTE) method is employed to the (2+1)-dimensional Caudrey—Dodd—Gibbon-Kotera—Sawada (CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.

Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions (or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.