Asymptotic models arising in cold-plasma equations

In this talk we will derive new asymptotic models for a hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. We also provide the well-posedness of these asymptotic models in Sobolev spaces and demonstrate the existence of a class of initial data which exhibit wave breaking for the unidirectional model. Time permitting I will also comment on some further future works regarding solitary wave solutions.