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The non-linear diffusion equation, structured by Burgers [1], was proposed for describing the turbulence [2], acoustic waves [3], thermo-viscous fluids [4], and water wave [5]. There are many computational methods for handling the problem, such as the variable separation method [6], explicit finite difference method [7], Cole-Hopf procedure transform [8], least-squares quadratic B-spline finite element method [9], shock-capturing finite difference method [10], tanh-coth method [11], Riccati equation rational expansion method [12], and others [13-20]. In this paper, we consider the following Burgers equation in 1-D case [21]:

A new technique for solving the 1-D burgers equation