Possibility of an Akhmediev breather decaying into solitons

Abstract

We consider the process by which a constant or wide-pulse solution of the nonlinear Schr\"odinger equation can become converted into an ensemble of solitons by modulational instability. This process is generally believed to be one important step in the generation of supercontinuum in optical fibers. Starting from the Akhmediev breather solution we study the conversion by two methods: One is pulse shape-oriented and uses the soliton relation between width and peak power. The other is eigenvalue-oriented and uses results from scattering theory. It becomes clear that an evolution according to the unmodified nonlinear Schr\"odinger equation, even in the presence of noise, will not lead to the transformation into solitons. If one takes the Raman effect into account, however, a conversion to a soliton gas takes place.