Study on the periodic solution of the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

Abstract

In the current work, we consider the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov (Z-K) equation which is used widely to explain the propagations of the waves arising in plasma physics. The variational theory together with the Hamiltonian method are employed to construct the periodic solution of the equation. As expected, the obtained solution agrees well with the solution by He's variational method, which strongly proves the correctness of the proposed method. Finally, we illustrate the solutions through one example in the form of 3-D and 2-D plots. The obtained results show that the method is simple but effective, which is expected to shed a bright light on the study of the nonlinear partial differential equations arising in physics.