Cherenkov radiation emitted by Kuznetsov-Ma solitons

Cherenkov radiation emitted by Kuznetsov-Ma soliton (KMS) with an arbitrary propagation constant in the presence of higher-order dispersions is studied analytically and numerically. We show that the third-order dispersion (TOD) yields asymmetric radiated bands, while the fourth-order dispersion (FOD) gives rise to symmetric radiated bands only when the value of FOD is positive. In contrast to radiations emitted by other localized waves, such a radiation emerges periodically in propagation, and can exhibit multi-frequency bands which depends strongly on the propagation constant of the KMS. We presented radiation conditions to calculate different frequency bands, which shows great agreement with numerical simulations. Important radiation features such as radiation frequencies, velocities, and distances are shown in phase diagrams. Our results could be helpful for controllable radiations in nonlinear fiber and other nonlinear systems.