Phase portrait of ion-acoustic waves for the modified Gardner (mG) equation

<p>Phase portrait for the dynamical system of&nbsp;the modified Gardner (mG) equation in nonextensive plasmas. There are four types of trajectories namely,&nbsp;supernonlinear homoclinic trajectory &nbsp;(SNHT) and supernonlinear periodic trajectory (SNPT)&nbsp;containing three equilibrium points with one separatrix, nonlinear periodic trajectory (NPT)&nbsp; and nonlinear homoclinic trajectory (NHT)&nbsp;containing one equilibrium point with no separatrix.</p>