Solitary and cnoidal solution of ZK equation in multicomponent magnetized dusty plasma with Fermi-Dirac electrons and positrons

The nature of nonlinear ion acoustic waves in multicomponent magnetized dusty plasma have been investigated theoretically. Species of modeled plasma include negative dust particle, ions, electrons and positrons. Both electrons and positrons obey Fermi-Dirac distribution function. Employing reduction perturbation method, the fluid equations was solved to achieve ZK equation. Solitary and cnoidal solution of ZK equation were considered due to number of roots of Sagdeev equation. Results show that both solitonic and cnoidal solutions of ZK equation are under the influence of considered quantumic effect of the modeled plasma. Amplitude of both generated modes in plasma medium varies noticeably with variation of quantum Bohm potential term.