  Resetting or restart, when applied to a stochastic process, usually brings
its dynamics to a time-independent stationary state. In turn, the optimal
resetting rate makes the mean time to reach a target to be the shortest one.
These and other intriguing problems have been intensively studied in the case
of ordinary diffusive processes over the last decade. In this paper we consider
the influence of stochastic resetting on a diffusive motion modeled in terms of
the non-linear differential equation. The reason for its non-linearity is the
power-law dependence of the diffusion coefficient on the probability density
function or, in another context, the concentration of particles. We briefly
outline this issue at first to prepare the foundations for our further
considerations. Then, we derive an exact formula for the mean squared
displacement and demonstrate how it attains the steady-state value under the
influence of exponential resetting. This mechanism brings also about that the
spatial support of the probability density function, which for the free
non-linear diffusion is confined to the set of a finite measure, tends to span
the entire domain of real numbers. In addition, we explore the first-passage
properties for the non-linear diffusion intermittent by the exponential
resetting and find analytical expressions for the mean first-passage time and
determine numerically the optimal resetting rate which minimizes the mean time
needed for a particle to reach a pre-determined target. Finally, we test and
confirm the universal property that the relative fluctuation in the mean
first-passage time of optimally restarted non-linear diffusion is equal to
unity.
