In this present study we obtained some new analytical solutions, such as trigonometric function, rational function, and hyperbolic function solutions by using of new extension of the (G'/G)-expansion method to the coupled (2 + 1)-dimensional Painlevé integrable Burgers equation with the aid of the computer software Maple. This method allows to carry out the solution process of nonlinear wave equations more thoroughly and conveniently by computer algebra systems such as the Maple and Mathematica. In addition, some figures of partial solutions are provided for direct-viewing analysis. The method can also be extended to other types of nonlinear evolution equations in mathematical physics
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