On the ZK equation with a directional dissipation

摘要

This paper studies the generalized Zakharov–Kuznetsov–Burgers equation. The initial value problem associated to this equation will be investigated in the nonhomogeneous Sobolev spaces and some suitable weighted spaces, under appropriate conditions. Moreover, an ill-posedness result (in some sense) will be proved in the anisotropic Sobolev spaces. Furthermore some exact traveling wave solutions of this equation will be obtained.