  We study nonlinear dynamics of coupled Skyrmions and present a method for
manipulating topological resonant excitations by a dual-frequency microwave
field. Thiele's equation is extended by introducing a new effective mass
associated with time derivative of topological density. Two coupled resonant
modes endowed with the new effective mass are found in the coupled Skyrmions.
Polygon-like resonant excitations are observed and modulated when the two modes
are activated simultaneously by microwave field with commensurate frequency
ratio. Quasiperiodic behavior of excitations are related to an incommensurate
ratio. Numerical solutions based on the extended Thiele's equation for Skyrmion
under a dual-frequency field agree well with the micromagnetic simulation
results and clarify the importance of frequency value, frequency ratio of an
external field and the effective mass to the polygon-like dynamics of Skyrmion.
We also show the coupling between two Skyrmions can dominate their topological
resonant excitations.
