Dynamics of soliton waves of group-invariant solutions through optimal system of an extended KP-like equation in higher dimensions with applications in medical sciences and mathematical physics

Abstract

The dynamics of solitons waves associated with higher-order nonlinear partial differential equations that model situations in physical systems obtainable in the fields of science and engineering help to understand the physical meaning of various soliton solutions obtained for these nonlinear differential equations. Thus, in this paper, we analytically investigate an extended Kadomtsev-Petviashvili-like equation existent in three dimensions. The robust technique of the Lie group theory of differential equation was invoked to achieve analytic solutions to the equation. This technique is used in a systematic way to generate the Lie point symmetries of the equation under study. Consequently, an optimal system of Lie subalgebra related to the equation is obtained. Thereafter, we engage the various gained subalgebras to reduce the Kadomtsev-Petviashvili-like equation to ordinary differential equations for the possibility of obtaining relevant closed-form solutions. Fortunately, various soliton solutions were found. These include different complex soliton solutions consisting of dark, bright, topological kink and singular. Some other solutions achieved are logarithmic, periodic and those which contain arbitrary functions. Therefore, to understand the physical meaning of these solutions, we depict them graphically. This exposed us to various wave structures which were later analyzed and applied. Moreover, we highlighted the significance of these solutions in various fields of science and engineering.