de la Cruz de Oña, Artorix2022-10-252022-10-252022-10-24http://hdl.handle.net/10222/82047The study of the light propagation in some complex media and its out-of-equilibrium dynamics is reported. Our research is based on the light-matter interaction hydrodynamic model under the multiscale expansion framework. At the proper scale of our mathematical analysis, the optical Benney-Luke equation is obtained. Also, we have proposed and demonstrated analytically, a novel and simpler variational approach to describe nonlinear open systems. Our methodology has been extended to the polarization instability effect on the beat length of propagating optical fields in a nonlinear birefringent Kerr medium. We have described the generation and dynamics of shock waves, specifically in disordered colloids. Finally, a preliminary theory based on reaction-diffusion dynamical system theory has been developed as a new goal for this project.enLIGHT PROPAGATIONNONLINEAR MEDIAThesis