In this thesis, we study extreme events in nonlinear systems, focusing on gravity waves on the surface of water and optical filamentation.

The first chapter provides a general introduction to nonlinear systems and their scientific interest, emphasizing their connection to extreme events in systems described by the nonlinear Schrödinger equation.

The second chapter focuses on the study of rogue waves, discussing a possible mechanism for stabilizing wave packets responsible for these waves by changing the depth of the water. However, our model does not allow us to draw conclusions about the impact of this mechanism on the distribution of wave heights under real conditions.

The third chapter presents an extension of the nonlinear Schrödinger equation to the fourth order, taking into account the contribution of the mean flux in deep and intermediate waters. We compare this extension to other versions already published in the literature, which underestimate the effect of the mean flux in deep water. We then extend the analysis to intermediate depths using simulations.

The fourth chapter studies optical filamentation, analyzing wavefront fluctuations induced by turbulence and the self-amplification of a laser beam beyond a critical energy density.

In conclusion, this thesis presents two different manifestations of nonlinearity and extreme events in deterministic and stochastic systems. Both phenomena can be studied using the nonlinear Schrödinger equation, illustrating the universality of nonlinearity in physical systems.