A variational principle for the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

Abstract

Abstract The Zakharov-Kuznetsov equation plays a key role in the plasma physics, and its solution has always been a hot topic, however its variational principle has not been studied. So this paper develops a variational formulation for the (3+1)-dimensional extended quantum Zakharov-Kuznetsov equation by the semi-inverse method, which shows an energy conservation law for the dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma. The whole derivation process is presented in detail. The obtained results in this paper are expected to shed a bright light on the study of theoretical basis for the magnetized plasma.