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The number of ultrahigh energy events at IceCube is estimated, for the firsttime, taking into account non-linear QCD effects in the neutrino - hadron crosssection. We assume that the extragalactic neutrino flux is given by$\Phi_{\nu}(E_{\nu})=\Phi_{0}E^{-2}_{\nu}$ and estimate the neutrino - hadroncross section using the dipole approach and a phenomenological model for thedipole - hadron cross section based on non-linear QCD dynamics. We demonstratethat the non-linear prediction is able to describe the current IceCube data andthat the magnitude of the non-linear effects is larger than 20 % for visibleenergies of order of 2 PeV and increases with the neutrino energy. Our mainconclusion is that the non-linear QCD effects are non-negligible and should betaken into account in the analysis of the number of ultrahigh energy events.

Estimating non-linear QCD effects in ultrahigh energy neutrino events at IceCube