Comment on "Solitonlike Solutions of the Grad-Shafranov Equation"

Abstract

In the above entitled recent publication by Giovanni Lapenta [Phys. Rev. Lett. Vol 90, 135005 (2003) ] it is claimed construction of a new class of solitonlike solutions for the Grad-Shafranov equation in plane geometry. It is proved here that, because of the mathematically erroneous choice \nabla p= |\Psi|^2 \Psi \nabla \Psi for an analytic continuation of the poloidal magnetic flux-function \Psi in the complex plane (p is the pressure), the cubic Schr\"odinger equation considered by the author is irrelevant to the equilibrium problem and the Grad-Shafranov equation.