Higher-order rogue-wave fission in the presence of self-steepening and Raman self-frequency shift

Abstract

Using the generalized nonlinear Schr\"odinger equation, we investigate how the effect of self-steepening and Raman-induced self-frequency shift impact higher-order rogue-wave solutions. We observe that each effect breaks apart the higher-order rogue wave, reducing it to its constituent fundamental parts, in a similar manner to how a higher-order soliton undergoes fission. Applying a local inverse-scattering technique, we show that under the effect of self-frequency shift, the emergence of a rogue wave significantly influences the surrounding wave background, triggering solitons, breathers, and new rogue waves. We demonstrate that under the combined effect of third-order dispersion, self-steepening, and Raman-induced self-frequency shift, the disintegrated elements of higher-order rogue waves become fundamental solitons, creating an asymmetrical spectral profile that generates both red- and blue-shifted frequency components. We also show the intermediary processes of the fission steps prior to soliton transformation which can only be observed in the presence of weak perturbations. These observations reveal the mechanisms that create a large number of solitons in the process of modulation instability-induced supercontinuum generation from a continuous-wave background in optical fibers.