Linear and Nonlinear Dust Ion Acoustic Waves in a Dense Quantum Magneto Plasma

In this article, linear and nonlinear dust ion acoustic (DIA) waves are studied in a magnetized quantum dusty plasma which consists of inertialess electrons and positrons, cold ions and negatively charged dust grains. For this purpose, quantum Hydrodynamic model (QHD) and reductive perturbation method are employed. To investigate linear and nonlinear waves, dispersion relation and a quantum Zakharov-Kuznetsov (ZK) equation are derived respectively. A stationary solution of the ZK equation is obtained to investigate the effects of plasma parameters on the amplitude of the solitons.