Stability Analysis of Steady State Solutions of Sine–Gordon Equation

The stability analysis of steady state solutions of SineGordon equation using Fourier mode stability analysis in two cases has been considered : Firstly when the amplitude is constant and secondly when the amplitude is variable in the two cases the results were found to be : The steady state solutions and are unconditionally stable . In the second case the comparison between the analytical solution and the numerical solution of Galerkin technique has been done . This comparison showed that the analytical solution and the numerical solution of Galerkin technique are the same.