English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the year 2003 a paper by G. Lapenta demonstrated that there is a new classof soliton-like solutions for the Grad-Shafranov Equations (GSE).The authordetermined an appropriate pair of transformations of the free fields p (fluidfield of hydrodynamical pressure) and Bz (z- component of magnetic inductionfield) that leads from the Helmholtz Equation to the Non-Linear SchroedingerEquation (NLSE) with cubic non- linearity. In the following year (2004), thework of Lapenta was opposed by G.N. Throumoulopoulos et al.,who criticized hisidea of the field transformations as a mathematically incoherent choice;contextually the authors suggested a new point of view for this one. In hisresponse, in the same year, G. Lapenta carried out numerical simulations thatshowed the existence of solitonic structures in a Magnetohydrodynamical (MHD)plasma-context. In the present work I want to demonstrate a critical conditionfor a complex poloidal flux function psi in a plane framework (x;y) that leadsto a class of pseudo-general NLSEs which establishes the validity of bothG.Lapenta and G.N. Throumoulopoulos et al. choices for the field transformationfunctionals.

From Grad-Shafranov equations set to a pseudo-general form of the non-linear Schroedinger equation