Figure 5.

Evolution and energy interaction plots along $z$ for the pump and its next three harmonics from Fig. 4a, b. The top blue curve in all examples represents the pump. (a) Pump ${\omega }_0$ exhibits energy exchange with neighboring sidebands $({\omega }_1,{\omega }_2,{\omega }_3)$ while maintaining recurrence behavior along $z$. (b) The harmonic ${\omega }_{12}$, excited at the resonant frequency ${\omega }_{R2}=17.26$, now acts as a pump (marked by the white arrow in Fig. 4a), interacting with sidebands $({\omega }_{11},{\omega }_{10},{\omega }_9)$ originating from its left side. Similarly, (c) illustrates the evolution of three sidebands $({\omega }_{13},{\omega }_{14},{\omega }_{15})$ on the right of ${\omega }_{12}$. (d) Shows the evolution of the first three sidebands $({\omega }_1,{\omega }_2,{\omega }_3)$ in Fig. 4b next to the pump ${\omega }_0$ with ${\beta }_4=0.1$, revealing energy exchange. (e) Displays the interaction of harmonic ${\omega }_8$ indicated by the white arrow as the pump with sidebands $({\omega }_7,{\omega }_6,{\omega }_5)$ situated on its left. Similarly, (f) shows the interaction of sidebands $({\omega }_9,{\omega }_{10},{\omega }_{11})$ with ${\omega }_8$ on the right.