Abstract
We give a comprehensive summary of the results on self-guided beams, bright spatial solitary waves, emphasizing the most recent advances. To be stable in a bulk medium, such beams should propagate in a non-Kerr medium. It is emphasized that all spatial solitons are generically the same, independent of the type of nonlinear medium, and such free-propagating beams can execute interesting dynamics, including spiraling around one another, self-tapering, periodically changing their shape, cross section, or polarization, and inelastically colliding to annihilate one another, fuse, or create a new beam. Most of these types of solitary-wave dynamics have recently been confirmed experimentally for self-guided beams propagating in different non-Kerr materials. Significantly, there exists no temporal analog (e.g., for pulse propagation in fibers) even for stationary spatial solitons of a bulk medium.
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