Dynamical analysis of lump solutions for (3 + 1) dimensional generalized KP–Boussinesq equation and Its dimensionally reduced equations

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Abstract
This paper analyzes a new form of the (3 + 1) dimensional generalized Kadomtsev–Petviashvili (KP)–Boussinesq equation for exploring lump solutions by making use of its Hirota bilinear form. The sufficient and necessary conditions for assuring analyticity, positiveness and rational localization of the solutions are developed in a uniform manner. Furthermore, the dimensionally reduced new form of the (3 + 1) dimensional generalized KP–Boussinesq equation has been also considered to establish lump solutions with free parameters, which play a vital role in influencing and controlling the phase shifts, propagation directions, shapes and energy distributions for these solutions. We have depicted the profile characteristics of extracted solutions by presenting some density plots, three-dimensional plots and two-dimensional plots for particular values of the free parameters involved.

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