Many applications, such as inertial confinement fusion, require an understanding of the physical mechanisms involved when high-energy laser beams propagate in a plasma. In particular, in the case of fusion, the aim is to quantify the deposition of laser energy on a cryogenic deuterium-tritium target, and the efficiency with which this target can be compressed to trigger fusion reactions. However, during their propagation, laser beams create a plasma wave that grows at the expense of the incident laser energy. However, the growth of this wave is not infinite and stops when the wave breaks up. This is accompanied by the production of hot electrons, which can preheat the target and hinder its compression. The breaking of a plasma wave is a physical phenomenon of the kinetic type, which can only be correctly described by calculating the velocity distribution of the electrons in the plasma. The aim of this thesis is to study wave breaking both theoretically and numerically, using Vlasov-type kinetic codes. One of the main difficulties lies in the discontinuity of the distribution functions to be described. In addition, it is necessary to describe the surge from its linear phase to the non-linear regime, enabling the creation of hot electrons to be quantified. The ultimate goal of the thesis is to produce models that are simple enough to run on the CEA's dimensioning codes.