Dynamical solitons in Bose-Einstein condensates

Solitons are principal characters in the dynamics of nonlinear media. By balancing the effects of dispersion against a nonlinear self-focusing, solitons are a class of waves which have abnormally high and isolated peaks while being abnormally persistent. These solitary waves have been realized in a variety of contexts including water tanks, optical fiber, magnetic materials and atomic gases in parallel with excellent agreement with applied mathematical models. These kinds of waves have long been sought as candidates for explaining rogue waves -- abnormally large waves responsible for capsizing vessels at sea. In this work, we create a unique type of soliton known as a Peregrine soliton in a quasi-one-dimensional Bose-Einstein condensate. We describe an experimental procedure for producing this soliton as well as numerical methods simulated the dynamical evolution of the wave.