Predicting PDF tails in systems with logarithmic non-linearity

The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These PDF tails are shown to be broader than a Gaussian distribution and are a manifestation of intermittency caused by short lived coherent structures (instantons).