Vi. Karpman et Jm. Vandenbroeck, STATIONARY SOLITONS AND STABILIZATION OF THE COLLAPSE DESCRIBED BY KDV-TYPE EQUATIONS WITH HIGH NONLINEARITIES AND DISPERSION, Physics letters. A, 200(6), 1995, pp. 423-428
Solitons of fifth order KdV-type equations with high nonlinearities ar
e investigated numerically by finite difference schemes. It is shown t
hat 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 th
e equation), solitons with sufficiently high nonlinearities in the equ
ations are shown to be unstable with respect to collapse-type instabil
ities, which agrees with the general theory of collapse. On the other
hand, the instabilities have not been detected in the presence of fift
h order dispersion, which shows that the latter plays a stabilizing ro
le.