Dr. Frédéric Valet
Laboratoire de Mathématiques dOrsay
Université Paris-Saclay, Francia

For some non-linear dispersive equations, waves can exhibit remarkable coherent structures, such as traveling waves or vortices. Those particular shapes are considered as fundamental bricks for the long-time description of the solutions.
Indeed, many solutions can be approximated by the help of those structures, using their stability properties or an adequate scaling. We will address the problem of finding those coherent structures for different equations, and discuss how finding those structures helps to understand the long-time dynamics of solutions.