Solitons in astrophysics

There are strong theoretical grounds and some supporting (but inconclusive) observational grounds for expecting solitons to occur in astrophysical plasmas, such as the Sun, the solar wind, and the magnetosphere. Solitons may arise whenever nonlinearity is balanced by dispersion. The large time and length scales of astrophysical plasmas favour the development of nonlinearity. Two causes of dispersion are reviewed, adopting the ideal MHD equations together with the generalized form of Ohm's law including the Hall current. Dispersion then arises either because of ion inertial effects or from inhomogeneities in the equilibrium state. A number of well-known equations are obtained including the Korteweg-de Vries, modified Korteweg-de Vries, derivative nonlinear Schroedinger, nonlinear Schroedinger, and Benjamin-Ono equations. The behaviour of both Alfven and magnetoacoustic waves is examined. (author)