Bifurcations of small-amplitude supernonlinear waves of the mKdV and modified Gardner equations in a three-component electron-ion plasma

Small-amplitude supernonlinear ion-acoustic waves (SIAWs) are examined in a multicomponent electron-ion plasma that is composed of fluid cold ions and two temperature q-nonextensive hot and cold electrons. Implementing the reductive perturbation method, four nonlinear evolution equations are derived: the Korteweg-de-Vries (KdV) equation, the modified KdV (mKdV) equation, the further modified KdV equation, and the modified Gardner (mG) equation. Employing the traveling wave transformation, the nonlinear evolution equations are deduced to their corresponding planar dynamical systems. Applying phase plane theory of dynamical systems, phase portrait profiles including nonlinear homoclinic trajectories, nonlinear periodic trajectories from the KdV equation, and additional supernonlinear periodic trajectories are presented for ion-acoustic waves (IAWs) from the modified KdV equation. Furthermore, supersolitons corresponding to the supernonlinear homoclinic trajectory of IAWs under the modified Gardner equation are shown in a phase plane and confirmed by the potential plot with a specified set of physical parameters q , σ c , σ h , f, and U. Nonlinear and SIAWs are displayed using computation for distinct parametric values.