ABSTRACT
Media without dispersion but with a large enough number of integrals of motion can also have solitary solutions whose constant shape is related to the existence of the integrals. This chapter discusses the class of toroidal Alfvén solitons whose shape can be found by numerical methods. Solitary magnetohydrodynamic (MHD) vortices can occur in the space plasmas, for example, in the solar wind which, since it is large and comparatively homogeneous, is a convenient object for studying Alfvén waves. V. I. Petviashvili, O. A. Pokhotelovand and N. V. Chudin and V. I. Petviashvili, O. A. Pokhotelov and L. Stenflo have found solutions to the MHD equations in the form of solitary toroidal vortices. The study of toroidal vortices has become especially important in connection with the development of the powerful quasistationary plasma-static and plasma-dynamic confinement systems in which hydrodynamic motion coexists with a solenoidal magnetic field.
