STABILITY OF COMPACTON SOLUTIONS

The stability of the recently discovered compacton solutions is studie d by means of both linear stability analysis as well as Lyapunov stabi lity criteria; From the results obtained it follows that, unlike solit ons, all the allowed compacton solutions are stable, since the stabili ty condition is satisfied for arbitrary values of the nonlinearity par ameter. The results are shown to be true even for the higher order non linear dispersion equations for compactons. Some conservation laws for the higher order nonlinear dispersion equations are also presented.