Initial-boundary value problems for the Zakharov-Kuznetsov equation and its modification

Initial-boundary value problems for the Zakharov-Kuznetsov equation and its modification for nonlinearity of higher order in the case of two spatial variables will be considered. Such equations describe nonlinear wave processes in dispersive media, when the waves propagate in one preassigned direction with deformations in the transversal direction. The main part of the presentation will be devoted to the recent results by the author concerning the problem on a half-strip, where the results are the most developed. The survey of previous results for other domains will be also presented.