Analytical soliton construction and dynamical transition analysis for the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony model

In the present work, an extensive analytical analysis is carried out to obtain new exact soliton solutions for the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The New Mapping Method (NMM), a recent, effective and robust technique for determining exact solutions of different nonlinear evolution equations is used. By empolying this technique, various new analytical solutions are obtained and represented by trigonometric and exponential functions. These solutions are new and different from those earlier documented in the literature. In addition, contour simulations are presented together with 2D and 3D graphical illustrations of the solution profiles showing that the solutions derived contain both singular and solitary wave forms. Graphical presentations of M-shape, kink, bell type, anti-bell type, singular wave, peakon and singular bell shape solutions for given parameter values are given. Finally, we apply the Galilean transformation to convert the ODE into a dynamical system. The behavior of the dynamical system is discussed using chaos and sensitivity analysis. To the best of present knowledge, the obtained solutions are important and can help in understanding new physical phenomena that are ruled by the KP-BBM equation.