Organizers of this minisymposium are
Many models involved in physics, such as in fluid dynamics, plasma physics or magnetism, are nonlinear evolution equations of dispersive or Hamiltonian type, as for Korteweg-de Vries equation or Schrödinger type and Landau-Lifshitz equations. The dynamics of such models is often governed by a subtle interplay between a linear (dispersive) part and a non-linearity, and is naturally organized around coherent, non-dispersive structures — solitons in the broad sense, encompassing travelling waves, ground states, dipoles, or topological solitons such as skyrmions and domain walls. A central question is their stability, understood as the persistence of these objects under perturbation of the initial data. While many integrable systems benefit from a description of their solitons and of the stability thereof, those techniques do not easily generalize to all physical models. This fosters the development of genuinely non-linear dynamical techniques. This mini-symposium aims to gather specialists to present their recent results on well-posedness, long-time behavior, and the stability of soliton-like structures for non-linear evolution equations. Given the growing interest in these questions, this event offers a good opportunity for researchers from various communities to exchange ideas and motivate new collaborations.