Abstract
In this research article, a new technique for solving nonlinear complex physical phenomena, arising in different fields of science, is investigated, called Modified extended mapping method. The method is applied to three dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation for the dust-ionacoustic waves in dusty plasmas. As a result, the exact and solitary wave solutions (which represent electric field potential), electric and magnetic fields and quantum statistical pressure for ZKB equation are obtained with the aid of Mathematica. These new exact solitary wave solutions are expressed in the forms of hyperbolic, trigonometric and rational functions. The graphical representations of the electric field potential and electric and magnetic fields are shown. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.