From rogue wave solution to solitons

Using a generalized nonlinear Schrodinger equation, we investigate the transformation of a fundamental rogue wave solution to a collection of solitons. Taking the third-order dispersion, self-steepening, and Raman-induced self-frequency shift as the generalizing effects, we systematically observe how a fundamental rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while a group of solitons are created. Applying a local inverse scattering technique based on the periodization of an isolated structure, we show that the third-order dispersion and Raman-induced self-frequency shift generates a group of solitons in the neighborhood where the rogue wave solution emerges. Using a volume interpretation, we show that the self-steepening effect stretches the rogue wave solution by reducing its volume. Also, we find that with the Raman-induced self-frequency shift, a decelerating rogue wave generates a red-shifted Raman radiation while the rogue wave itself turns into a slow-moving soliton. We show that when third-order dispersion, self-steepening, and Raman-induced self-frequency shift act together on the rogue wave solution, each of these effects favor the rogue wave to generate a group of solitons near where it first emerges while the rogue wave itself also becomes one of these solitons.

Automated summary

Using a generalized nonlinear Schrodinger equation, the study investigates how a fundamental rogue wave transforms into a collection of solitons. The effects of third-order dispersion, self-steepening, and Raman-induced self-frequency shift are considered, and it is observed that the rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while multiple solitons are created. The study also demonstrates that the combination of these effects favors the generation of solitons near the emergence of the rogue wave, with the rogue wave itself becoming one of these solitons.