“…Solitons (or, more properly, solitary waves) in Kerr-type focusing media are described by the cubic nonlinear Schrödinger (NLS) equation and they are known to be unstable in two and three dimensions because of the occurrence of the collapse of the wave packet (see, e.g., the review [4]). Various schemes to arrest the collapse were proposed such as the use of weaker saturable [5] or quadratic nonlinearities [6][7][8][9], or to use the concept of nonlinearity and group-velocity dispersion (GVD) management in tandem structures, which are composed of periodically alternating linear dispersive and quadratically nonlinear layers [10]. Other recent approaches use off-resonance two-level systems [11], self-induced-transparency media [12], inhomogeneous, dispersive nonlinear media (for example, a graded index Kerr medium [13]), or small negative fourth-order GVD to arrest the spatiotemporal collapse [14] (this scheme works only in two dimensions, that is, in a planar waveguide with pure Kerr nonlinearity).…”