Abstract
By applying the Lie symmetry method, abundant group-invariant solutions are constructed for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which provides a water wave model for long waves of small amplitude with weakly non-linear restoring forces and frequency dispersion. Infinitesimal generators of symmetries, the commutation table of the symmetry Lie algebra, and an optimal system of one-dimensional Lie symmetry sub-algebras are presented. The governing gKP equation is reduced into several nonlinear ordinary differential equations utilizing thrice symmetry reductions. Consequently, abundant group invariant solutions are obtained in the shapes of different dynamical wave structures of solitons, multi-solitons, W-shaped solitons, doubly solitons, kink-type solitons, lump-type solitons interaction between parabolic waves and lump solitons, and annihilation multi-solitons profiles. The physical interpretation of the resulting soliton solutions is illustrated by three dimensional graphical through numerical simulation. The obtained group-invariant solutions involve many arbitrary functions, thereby exhibiting rich physical structures and including the existing solutions in the literature.