STATIONARY SOLITONS AND STABILIZATION OF THE COLLAPSE DESCRIBED BY KDV-TYPE EQUATIONS WITH HIGH NONLINEARITIES AND DISPERSION

Solitons of fifth order KdV-type equations with high nonlinearities are investigated numerically by finite difference schemes. It is shown that the soliton asymptotics may be both monotonically and oscillatory decaying, in agreement with analytical predictions. In the absence of higher order dispersion (i.e. without the fifth order derivative in the equation), solitons with sufficiently high nonlinearities in the equations are shown to be unstable with respect to collapse-type instabilities, which agrees with the general theory of collapse. On the other hand, the instabilities have not been detected in the presence of fifth order dispersion, which shows that the latter plays a stabilizing role.