从Grad-Shafranov方程组到伪一般形式的非线性Schroedinger方程
From Grad-Shafranov equations set to a pseudo-general form of the non-linear Schroedinger equation
摘要：
2003年G. Lapenta证明了Grad-Shafranov方程（GSE）存在一类新的类孤子解，作者确定了一对合适的自由场p（流体压力场）和Bz（磁感应场的z分量）的变换，将Helmholtz方程转化为具有立方非线性的非线性Schroedinger方程（NLSE）。在接下来的一年（2004年），Lapenta的工作遭到了G.N.的反对。Throumoulopoulos等人，他批评他的场变换的想法是一个数学上不连贯的选择;根据上下文，作者对此提出了一个新的观点。在他的回应中，同年，G。Lapenta进行了数值模拟，显示了磁流体动力学（MHD）等离子体背景下的孤子结构的存在。在目前的工作中，我想证明一个复杂的极向通量函数psi在一个平面框架（x;y）的临界条件，导致一类伪一般NLSE建立的有效性G.Lapenta和G. N。场变换泛函的选择。
英文摘要：
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.
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