Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma

• The dust–ion-acoustic waves with high-energy electrons and positrons is considered.
• The Zakharov–Kuznetsov–Burgers equation by reductive perturbation method is obtained.
• Nonlinear wave solutions of the three-dimensional ZKB equation are obtained.
• We discussed the stability analysis for these solutions.

The propagation of dust–ion-acoustic waves with high-energy electrons and positrons in three-dimensional is considered. The Zakharov–Kuznetsov–Burgers (ZKB) equations for the dust–ion-acoustic waves in dusty plasmas is obtained. The conservations laws and integrals of motion for the ZKB equation are deduced. In the present study, by applying the modified direct algebraic method, we found the electric field potential, electric field and quantum statistical pressure in form water wave solutions for three-dimensional ZKB equation. The solutions for the ZKB equation are obtained precisely and efficiency of the method can be demonstrated. The stability of the obtained solutions and the movement role of the waves by making the graphs of the exact solutions are discussed and analyzed.