Phase portrait, multi-stability, sensitivity and chaotic analysis of Gardner’s equation with their wave turbulence and solitons solutions
Adil Jhangeer, Muhammad Muddassar, Jan Awrejcewicz, Zarmeena Naz, Muhammad Bilal Riaz
Abstract
The Gardner’s equation is investigate in this article, and numerous unique solutions are discover by utilizing direct-algebraic technique. We can view a big series of innovative outcomes in a more intuitive and simple way than with the old method for executing Gardner’s solutions. Many solitons solution are obtain and evaluate by using various software like Mathematica, maple and MATLAB. We use Mathematica for obtain solution representation of 2D, 3D graphs. After that, we use Galilean transformation to transform the system into a planer dynamical system. All potential examples of phase portraiture are represent by graphs in terms of the parameters. Furthermore, our recent job is actually enquiry quite advantageous and valuable in supporting us in fixing concerns including shock waves, solitonic behaviour, and so on. We apply sensitive analysis theory, which offers us with a wide range of linear periodic and first rate periodic character. In this paper, sensitivity analysis, chaos analysis, and multi-stability analysis of Gardner’s equation are examine.