Bifurcations of nonlinear and supernonlinear ion-acoustic waves (IAWs) are studied in an electron-ion plasmas with generalized (r, q)-distributed electrons. The IAWs are examined under the Zakharov–Kuznetsov (ZK) and modified ZK equations using the reductive perturbation technique. Transforming both the ZK and mZK equations into their corresponding dynamical systems, all possible phase spaces and potential energy functions are analyzed. The nonlinear periodic and solitary wave solutions are obtained under the ZK and mZK equations. A newly discovered supernonlinear wave, in particular, supernonlinear periodic wave under the modified ZK equation in electron-ion magnetized plasma with (r, q)-distributed electrons is reported for the first time in the literature. Nonlinear and supernonlinear wave solutions are shown under the influence of physical parameters. The proposed study contributes to new wave motions in slow solar wind streams and astrophysical plasmas.
