The Cauchy problem for the generalized Zakharov–Kuznetsov equation on modulation spaces

We consider the Cauchy problem for the generalized Zakharov–Kuznetsov equation ∂ t u + ∂ x 1 Δ u = ∂ x 1 ( u m + 1 ) on three and higher dimensions. We mainly study the local well-posedness and the small data global well-posedness in the modulation space M 2 , 1 0 ( R n ) for m ≥ 4 and n ≥ 3 . We also investigate the quartic case, i.e., m = 3 .