Initial-boundary value problems for the Zakharov-Kuznetsov equation in the plane and in space.

The Zakharov-Kuznetsov equation is a generalization of the Korteweg-de Vries equation to the case of several spatial variables. It models the propagation of nonlinear waves in a dispersive medium in a given direction, with the waves experiencing deformations in transverse directions. This talk will provide a brief historical overview of results on initial-boundary value problems for this equation in the cases of two and three spatial variables. The focus will be on the author's recent results in the spatial case, specifically addressing issues of global solvability and well-posedness of initial-boundary value problems, as well as the decay of solutions at large times.