Analytic study of (3+1) - dimensional Kadomstev-Petviashvili-Boussinesq equation: Painlevé analysis and exact solutions

In this article, (3+1) - dimensional Kadomstev-Petviashvili (KP) - Boussinesq equation, representing propagation of waves in nonlinear and dispersive media, is examined by locating movable critical points with aid of Painlevé analysis and it has been found that this equation passes Painlevé test which implies affirmation towards the complete integrability. Bilinear equation is constructed through truncated Painlevé expansion along with Bell polynomial approach, which further enriches the solution structure and then abundant exact solutions involving various arbitrary constants are furnished in uniform manner by using novel test function. It is worth to mention that completely new and different solutions are obtained from those reported in the literature.