Waves that appear from nowhere - rogue waves in optics

In this work, examples of exact solitary wave solutions of the nonlinear Schrodinger equation that "appear from nowhere" are presented. Two examples of such solutions . The amplitude of each of these solutions can take arbitrarily high values that depend on initial conditions. These properties of solutions make them a very likely explanation for the "rogue waves" in the ocean, since these also may have unusually high amplitudes and appear "from nowhere". A strong application for these results is the generation of exceptionally high amplitude optical pulses - "optical rogue waves".