Hard soliton excitation regime: Stability investigation

The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element of the four-wave interacti on has an additional smallness, is studied. It is that shown for optical so litons striction can weaken the Kerr nonlinearity. It is shown that soliton s with a finite amplitude discontinuity at the critical soliton velocity, e qual to the minimum phase velocity of linear waves, are unstable while soli tons with a soft transition remain stable with respect to one-dimensional p erurbations. Two- and three-dimensional solitons near threshold are unstabl e with respect to modulation perturbations. (C) 1999 American Institute of Physics. [S1063-7761(99)02207-6].