Stability Analysis for Steady State Solutions of Burger Equation

The Stability Analysis of Steady State Solution of Burger equation by using Fourier mode Stability analysis in two cases has been considered , the first one when the amplitude is constant and the second one when the amplitude is variable .
In the first case the steady state solution is always stable and the second case is conditionally stable . In the second case the comparison between the analytical solution and numerical solution of Galerkin technique are the same.