Self-focusing instability of two-dimensional solitons and vortices

The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970)] of one-dimensional acoustic solitons in media with positive dispersion. At large distances between vortices this instability transforms into the Crow instability [S.C. Crow, AIAA J. 8, 2172 (1970)] of two vortex filaments with opposite circulations. (C) 1995 American Institute of Physics.