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We consider nonlinear dynamics of a single vortex in a superconductor in astrong rf magnetic field $B_0\sin\omega t$. Using the London theory, wecalculate the dissipated power $Q(B_0,\omega)$, and the transient time scalesof vortex motion for the linear Bardeen-Stephen viscous drag force, whichresults in unphysically high vortex velocities during vortex penetrationthrough the oscillating surface barrier. It is shown that penetration of asingle vortex through the ac surface barrier always involves penetration of anantivortex and the subsequent annihilation of the vortex antivortex pairs.Using the nonlinear Larkin-Ovchinnikov (LO) viscous drag force at higher vortexvelocities $v(t)$ results in a jump-wise vortex penetration through the surfacebarrier and a significant increase of the dissipated power. We calculate theeffect of dissipation on nonlinear vortex viscosity $\eta(v)$ and the rf vortexdynamics and show that it can also result in the LO-type behavior,instabilities, and thermal localization of penetrating vortex channels. Wepropose a thermal feedback model of $\eta(v)$, which not only results in the LOdependence of $\eta(v)$ for a steady-state motion, but also takes into accountretardation of temperature field around rapidly accelerating vortex, and along-range interaction with the surface. We also address the effect of pinningon the nonlinear rf vortex dynamics and the effect of trapped magnetic flux onthe surface resistance $R_s$ calculated as a function or rf frequency andfield. It is shown that trapped flux can result in a temperature-independentresidual resistance $R_i$ at low $T$, and a hysteretic low-field dependence of$R_i(B_0)$, which can {\it decrease} as $B_0$ is increased, reaching a minimumat $B_0$ much smaller than the thermodynamic critical field $B_c$.

Dynamics of vortex penetration, jumpwise instabilities and nonlinear surface resistance of type-II superconductors in strong rf fields