Self-focusing instability of two-dimensional solitons and vortices
Kuznetsov E.A., Rasmussen J.
In the framework of the three-dimensional nonlinear Schrodinger equation (NLSE) the instability of two-dimensional solitons and vertices is demonstrated. The instability can be considered as the analog of the Kadomtsev-PetviashvjH instability  of one-dimensional acoustic solitons in media with positive dispersion. For large distance between the vortices this instability transforms into the Grow instability  of two vortex filaments with opposite circulations.