Natural curvilinear coordinates for ideal magnetohydrodynamics equations. Solutions with constant total pressure

Details Natural curvilinear coordinates for ideal magnetohydrodynamics equations. Solutions with constant total pressure Natural curvilinear coordinates for ideal magnetohydrodynamics equations. Solutions with constant total pressure

2010-08-06

arxiv.org/abs/1008.1124v1

Physics Letters A. Volume 375, Issue 3, 17 January 2011, Pages 283-290

Physics

Mathematical Physics

24 pages, 2 figures, 1 table

Scientific paper

10.1016/j.physleta.2010.11.022

Equations of magneto-gasdynamics in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the nonlinear vector wave equation coupled with the incompressibility condition in the form of the generalized Cauchy integral. The symmetry group of obtained equation, equivalence transformation, and group classification with respect to the constitutive equation are calculated. New exact solutions with functional arbitrariness describing non-stationary incompressible flows with constant total pressure are given by explicit formulae. The corresponding magnetic surfaces have the shape of deformed nested cylinders, tori, or knotted tubes.

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