Symbolic computation on the multi-soliton-like solutions of the cylindrical Kadomtsev–Petviashvili equation from dusty plasmas

Considering the transverse perturbation and axially non-planar geometry, the cylindrical Kadomtsev–Petviashvili (KP) equation is investigated in this paper, which can describe the propagation of dust-acoustic waves in the dusty plasma with two-temperature ions. Through imposing the decomposition method, such a (2+1)-dimensional equation is decomposed into two variable-coefficient (1+1)-dimensional integrable equations of the same hierarchy. Furthermore, three kinds of Darboux transformations (DTs) for these two (1+1)-dimensional equations are constructed. Via the three DTs obtained, the multi-soliton-like solutions of the cylindrical KP equation are explicitly presented. Especially, the one- and two-parabola-soliton solutions are discussed by several figures and some effects resulting from the physical parameters in the dusty plasma and transverse perturbation are also shown.