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Plasma waves are descriptions of mathematical forms that showing small perturbations far from the equilibrium of plasma. The equilibrium occur when some plasma parameters such as density and magnetic eld is constant according to the time function. The small perturbations will be reviewed in the Sine-Gordon Equation (SGE). SGE is a second order non linear Partial Dierential Equation (PDE) that has multiple solutions. A numerical approach is used to obtain the solution. Then the solution obtained are visualized using MATLAB program. The nal result of applying the numerical approach shows hyperbolic plasma waves and shows that analytical and numerical approach give the same solution but the numerical approach can only shows the perturbation for very small time function.