Quasi-periodic, strange chaotic behaviors, and soliton solutions of the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Abstract

Soliton solutions and chaotic analysis in integrable equations have become a hot topic in recent years. This work presents the qualitative dynamics and analytical solutions of (4+1)-D Boiti-Leon-Manna-Pempinelli (BLMP) model. Utlizing dynamical system approach, the mathematical analysis is performed. The given model is transformed into system of nonlinear ordinary differential equations (ODEs) via the Galilean transform. We study the bifurcations, quasi-periodic and chaotic dynamics, return maps, power spectrum, and strange attractors of the proposed model. Moreover, the soliton solutions are obtained with applications of the Khater method and the modified extended Tanh-function method (METM). The obtained results are illustrated in detail through 2D and 3D graphical representations.