Dynamic analysis of lump solutions based on the dimensionally reduced generalized Hirota bilinear KP-Boussinesq equation

Abstract

In this paper, a [Formula: see text]-dimensional generalized KP-Boussinesq equation is introduced and its associate Hirota bilinear form is also given. Based on finding the positive quadratic function solutions of the associate Hirota bilinear equation, the lump solutions of the proposed [Formula: see text]-dimensional generalized KP-Boussinesq equation and its corresponding reduced equations in [Formula: see text] dimensions are obtained. Furthermore, the sufficient and necessary conditions for guaranteeing the analyticity and rational localization of lump solutions are derived and expressed in the form of free parameters, which are involved in lump solutions and play a key role in controlling the dynamic properties of lump solutions. The localized properties are also analyzed and shown graphically.