New exact periodic elliptic wave solutions for extended quantum Zakharov–Kuznetsov equation

In this paper, the exact solutions of extended quantum Zakharov–Kuznetsov (QZK) equation which arises in hydrodynamic that describe the nonlinear propagation of the quantum ion-acoustic waves have been procured. The trial equation method with the discrimination system of polynomials is employed to find the analytical solutions. The local time fractional derivative is used in place of ordinary derivatives to get fractional model. Some plentiful new exact traveling wave solutions of nonlinear extended QZK equation are constructed. The solutions consist of singular, Jacobi elliptic and dark soliton solutions. Furthermore, the constraint conditions for the existence of these solutions are also presented.