From Grad-Shafranov equations set to a pseudo-general form of the non-linear Schroedinger equation
Abstract
Description
In the year 2003 a paper by G. Lapenta demonstrated that there is a new class of soliton-like solutions for the Grad-Shafranov Equations (GSE).The author determined an appropriate pair of transformations of the free fields p (fluid field of hydrodynamical pressure) and Bz (z- component of magnetic induction field) that leads from the Helmholtz Equation to the Non-Linear Schroedinger Equation (NLSE) with cubic non- linearity. In the following year (2004), the work of Lapenta was opposed by G.N. Throumoulopoulos et al.,who criticized his idea of the field transformations as a mathematically incoherent choice; contextually the authors suggested a new point of view for this one. In his response, in the same year, G. Lapenta carried out numerical simulations that showed the existence of solitonic structures in a Magnetohydrodynamical (MHD) plasma-context. In the present work I want to demonstrate a critical condition for a complex poloidal flux function psi in a plane framework (x;y) that leads to a class of pseudo-general NLSEs which establishes the validity of both G.Lapenta and G.N. Throumoulopoulos et al. choices for the field transformation functionals.
This paper has been showed in the context of 5th Workshop on Nonlinear Physics in Gallipoli (2008)
This paper has been showed in the context of 5th Workshop on Nonlinear Physics in Gallipoli (2008)