Long dynamo waves

A simple mean-field model of magnetic field generation in the Sun is considered. The model is characterized by spatially disjoint locations of the α and ω effects, believed to take place in the solar convection zone and in the solar tachocline, respectively, and includes α-quenching. The model admits a long wave dynamo instability, whose evolution is described by a perturbed mKdV equation. Solutions of this equation, the so-called snoidal waves, describe nonlinear waves of magnetic activity migrating towards the equator, as observed in the Sun.