Soliton instability and collapse in media with defocusing nonlinearity

The nonlinear Schroedinger equation is used to show that, for media with defocusing nonlinearity, one-dimensional solitons are unstable with respect to transverse modulations. The instability is analogous to the Kadomtsev-Petviashvili instability of sound solitons in media with weak positive dispersion. It is found that, for low-amplitude solitons, the nonlinear stage of development of the instability is one of collapse. An integral criterion of collapse is obtained.