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Lie symmetry analysis of the Grad-Shafranov equation

By Mehdi Nadjafikhah and Parastoo Kabi-Nejad

Abstract

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose the Grad-Shafranov equation which may illustrate the reciprocal advantage of this interaction between plasma physics and symmetry techniques. A symmetry classification of the Grad-Shafranov equation with two arbitrary functions $F(u)$ and $G(u)$ of the unknown variable $u=u(x,t)$ is given. The optimal system of one-dimensional subalgebras is performed. This latter provides a process for building new solutions for the equation.Comment: 9 page

Topics: Mathematics - Analysis of PDEs, 34C14, 35J05, 70G65
Year: 2011
OAI identifier: oai:arXiv.org:1105.1497
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