We investigate potential quantum nonlinear corrections to Diracs equation through its sub-leading effect on neutrino oscillation probabilities. Working in the plane-wave approximation and in the $mu-tau$ sector, we explore various classes of nonlinearities, with or without an accompanying Lorentz violation. The parameters in our models are first delimited by current experimental data before they are used to estimate corrections to oscillation probabilities. We find that only a small subset of the considered nonlinearities have the potential to be relevant at higher energies and thus possibly detectable in future experiments. A falsifiable prediction of our models is an energy dependent effective mass-squared, generically involving fractional powers of the energy.
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