Abstract
In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painlevé analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE by employing the Lie symmetry analysis. We formally derive bright, dark and singular soliton solutions of the model. Moreover, we investigate the stability of the corresponding dynamical system via using phase plane theory. Graphical representation of the obtained solitons and phase portrait are illustrated by using Maple software.
•The Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect is investigated.•The Painlevé and Lie symmetry analysis are applied to that equation.•The stability of the corresponding dynamical system is discussed via phase plane theory.•A graphical representation of the obtained soliton solutions is presented.