  We for the first time demonstrate that the widely existed nonlinear waves
such as rogue waves, contain Dirac monopoles. We find that the density zeros of
these nonlinear waves on an extended complex plane can constitute the Dirac
virtual magnetic monopole fields with a quantized flux of elementary $\pi$. We
then can explain the exotic property of ``appearing from nowhere and
disappearing without a trace" of rogue waves by means of a Dirac monopole
collision mechanism. The maximum amplification ratio and multiple phase steps
of high-order rogue waves are found to be closely related to the number of
their contained monopoles. Important implications of the intrinsic virtual
magnetic monopole fields are discussed.
