Lie Symmetry Analysis for Soliton Solutions of Generalised
Kadomtsev-Petviashvili-Boussinesq Equation in (3+1)-dimensions
Abstract
The Lie group of infinitesimal transformations technique and similarity
reduction is performed for obtaining an exact invariant solution to
generalized Kadomstev-Petviashvili-Boussinesq (gKPB) equation in
(3+1)-dimensions. We obtain generators of infinitesimal transformations,
which provide us a set of Lie algebras. In addition, we get geometric
vector fields, a commutator table of Lie algebra, and a group of
symmetries. It is observed that the analytic solution (closed-form
solutions) to the nonlinear gKPB evolution equations can easily be
treated employing the Lie symmetry technique. A detailed geometrical
framework related to the nature of the solutions possessing traveling
wave, bright and dark soliton, standing wave with multiple breathers,
and one-dimensional kink, for the appropriate values of the parameters
involved.