Phase portrait and potential energy function of the dynamical system corresponding to modified ZK equation for ion-acoustic waves in a magnetized electron-ion plasma with generalized (r, q) distributed electrons

<p>These figures (a) and (b) represent phase portrait and potential energy function of the dynamical system corresponding to the mZK equation&nbsp;for ion-acoustic waves in a magnetized electron-ion plasma with generalized (r, q) distributed electrons for q = 5 and r = 0.1. These figures contain&nbsp;three fixed points P_0,&nbsp;P_1&nbsp;and P₂&nbsp;with one&nbsp;separatrix. The figure (a) contains one family of supernonlinear periodic orbits, two families of periodic orbits and one pair of homoclinic orbits at&nbsp;P_{0.&nbsp;&nbsp;}The figure (b) contains the potential energy function with&nbsp;two local minima and one maxima which is necessary condition for supernonlinear wave.&nbsp;&nbsp;</p>