The Kerr-nonlinearity (KNL) or Kerr-effect is physically caused by the dependency of the refractive index on the field amplitude.

Starting from a reduced nonlinear Schroedinger equation without dispersion and attenuation $$ \frac{\partial q\left(t,z\right)}{\partial z} = -\mathrm{j}\gamma \left| q\left(t,z \right) \right|^2 q\left(t,z \right) $$ This differential equation is solved by $$ q\left(t,z\right) = q\left(t,z=0\right)\cdot\mathrm{exp}\left\{-\mathrm{j}\gamma\vert q\left(t,z=0\right)\vert^2z\right\} $$ From this equation it can be seen that the KNL causes a phase rotation depending on the instantaneous power of the signal.

In the frequency domain this phase rotation causes spectral broadening. The further the signal propagates the higher the effective bandwidth of the signal and therefore bigger bandwidth at the receiver is required. This effect is the reason for the increase in errors with higher input power when working in the nonlinear regime of the fiber.