Lie symmetry analysis and propagation of new dynamics of a negative-order model describing fluid flow

Abstract

This research is focused into the exploration of the inherent nonlinear dynamics related to the negative-order (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation. The simplified Hirota method is employed to construct and visualize the multiple solitons through phase portraits. The underlying methodology is advantageous as the model is not needed to convert in bilinear form. The symmetry analysis and the corresponding invariant solutions for the analyzed model are calculated using Lie groups. The underlying model is converted into second-order ordinary differential equation, which is further converted into the dynamical system of first-order differential equations through the utilization of Galilean transformation. Additionally, the qualitative examination of the acquired dynamical system is executed by employing the concept of bifurcation analysis. Following this, an external force is introduced to the model in order to generate a disruption, consequently leading to the formation of a perturbed dynamical system. The confirmation of chaotic behavior in the perturbed dynamical system is observed by employing a range of tools designed to detect chaos. The findings of this piece of research are highly captivating and provide a significant contribution to the field of soliton dynamics in particular and mathematical physics in general.

Keywords

• Symmetry reductions and invariant solutions
• Multi-solitons
• Bifurcation
• Chaotic behavior
• Negative-order KDV–CBS equation
• Simplified Hirota method