Propagation of electrostatic potential with dynamical behaviors and conservation laws of the (3+1)-dimensional nonlinear extended quantum Zakharov-Kuznetsov equation

The (G'/G)-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov-Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron-positron-ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge-Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented.