Solitonlike solutions of the Grad-Shafranov equation

A new class of solitonlike solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schrödinger equation for nonlinear wave propagation forms the basis to derive the new class of solutions. The solitonlike solutions are considered for their possible relevance to astrophysics and solar physics problems. We discuss how a solitonlike 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.