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By employing the quantum hydrodynamic model and the reductive perturbation technique, a quantum Zakharov-Kuznetsov (QZK) equation is derived for finite but small amplitude ion-acoustic waves in a quantum magnetoplasma. The extended Conte’s truncation method is used to obtain the solitary, explosive, and periodic solutions of the QZK equation. Furthermore, the stability of the solitary wave solution of the QZK equation is investigated by using the small-k perturbation expansion method.