A set of three coupled nonlinear differential equations describing low‐frequency (∂/∂t≪&OHgr;i, &OHgr;ibeing the ion gyrofrequency), electromagnetic perturbations slowly varying (∂/∂z≪∇⊥) along the external magnetic fieldB0ezin a homogeneous plasma is derived using a two‐fluid description. The equations are valid over a wide range of &bgr; (ratio of the electron thermal pressure and the magnetic pressure) and in proper limits reduce to the Hasegawa–Mima and convective cell equations, respectively. A general traveling solution for the full set of equations is described and studied in detail for the axially antisymmetric (dipole) case, when the only possible solution propagating with a finite velocity perpendicular to the external magnetic field has the form of a double vortex. There are two modes of vortices. The first one reduces to the Hasegawa–Mima modon in the limitvz=0, while the other in the limitvz=cA(Alfve´n speed) has zero density perturbation and can be identified as a generalized convective cell.