  The interaction of a magnetic vortex with a rotating magnetic field causes
the nucleation of a vortex--antivortex pair leading to a vortex polarity
switching. The key point of this process is the creation of a dip, which can be
interpreted as a nonlinear resonance in the system of certain magnon modes with
nonlinear coupling. The usually observed single-dip structure is a particular
case of a multidip structure. The dynamics of the structure with $n$ dips is
described as the dynamics of nonlinearly coupled modes with azimuthal numbers
$m=0,\pm n,\pm 2n$. The multidip structure with arbitrary number of vortex
antivortex pairs can be obtained in vortex-state nanodisk using a space- and
time-varying magnetic field. A scheme of a possible experimental setup for
multidip structure generation is proposed.
