Variational Iteration Method in Solving Evolution Equations Anwar Ja'afar Mohamed - Jawad Electrical Engineering Department, University of Technology, Baghdad, Iraq E-mail: anwar_jawad2001@yahoo.com Abstract This paper applies the Variational Iteration Method (VIM) to obtain solution of Evolution Equations (linear and nonlinear partial differential equations). The nonlinear model is considered Gas Dynamics equation and Burger's equation. The linear model is the Heat transfer (diffusion) equation. Results show that variational iteration method is a powerful mathematical tool for solving linear and nonlinear partial differential equations, and therefore, can be widely applied in engineering problems. Keywords: Variational Iteration Method, Gas Dynamics equation, Partial Differential Equation, Burger's Equation. Heat transfer Equation. PACS: AMS Classification: 35F25 INTRODUCTION Nonlinear phenomena play a crucial role in applied mathematics and physics. It is difficult to obtain the exact solution for these problems. In recent decades, there has been great development in the numerical analysis [1] and exact solution for nonlinear partial Differential Equations PDEs. There are many standard methods for solving Linear and nonlinear PDEs [19]; for instance, Backland transformation method [2], Lie group method [3] and Adomian’s decomposition method [4], inverse scattering method [5], Hirota’s bilinear method [6], homogeneous balance method [7] and He's homotopy perturbation method (HPM) [9, 10, 11, 12, 13, 14, and 20]. VIM was first proposed by He's [8, 15, 16, 18, and 21]; unlike classical techniques, nonlinear equations are solved easily and more accurately via VIM. This method has recently been applied to engineering equations [17]. In this paper, the VIM method is applied to solve two nonlinear partial differential equations PDEs and one linear partial differential equation. The first equation is the homogenous gas dynamics equation defined as: 0 , 1 0 0 ) 1 (            t x u u x u u t u (1) With initial condition ) ( ) 0 , ( x g x u  (2) Hossein etal [14] have solved Eq.(1) using Homotopy-perturbation method HPM, while Evans and Bulut [22] have solved it using Adomian decomposition method ADM. The second equation is the well-known nonlinear Burger's equation: 0 , 1 0 , 0 , 2 2             t x x u x u u t u   (3) with initial and boundary condition given by: