Soliton-Like Solutions of the Grad-Shafranov Equation
arXiv:astro-ph/0303448 · doi:10.1103/PhysRevLett.90.135005
Abstract
A new class of soliton-like solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schrödinger (CS) equation for non-linear wave propagation forms the basis to derive the new class of solutions. The soliton-like solutions are considered for their possible relevance to astrophysics and solar physics problems. We discuss how a soliton-like solution can be generated by a repetitive process of magnetic arcade stretching and plasmoid formation induced by the differential rotation of the solar photosphere or of an accretion disk.
Accepted for publication on Physical Review Letters