Self-focusing and transverse instabilities of solitary waves

We give an overview of the basic physical concepts and analytical methods for investigating the symmetry-breaking instabilities of solitary waves. We discuss self-focusing of spatial optical solitons in diffractive nonlinear media due to either transverse (one more unbounded spatial dimension) or modulational (induced by temporal wave dispersion) instabilities, in the framework of the cubic nonlinear Schrödinger (NLS) equation and its …