  We study on the relations between modulational instability and several
well-known nonlinear excitations in a nonlinear fiber, such as bright soliton,
nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and
Kuznetsov-Ma breather. We present a quantitative correspondence between them
based on the dominant frequency and propagation constant of each perturbation
on a continuous wave background. Especially, we find rogue wave comes from
modulational instability under the "resonance" perturbation with continuous
wave background. These results will deepen our understanding on rogue wave
excitation and could be helpful for controllable nonlinear wave excitations in
nonlinear fiber and other nonlinear systems.
