Exact Solutions for Some Partial Differential Equations by Using First Integral Method

In this paper, some exact solutions for the convectiondiffusionreaction equation in two dimensions and a nonlinear system of partial differential equations are formally derived by using the first integral method, which are based on the theory of commutative algebra. Keywords: First integral method; two-dimensional convectiondiffusionreaction equation, nonlinear system of partial differential equation.