Natural curvilinear coordinates for ideal magnetohydrodynamics equations. Solutions with constant total pressure
arXiv:1008.1124 · doi:10.1016/j.physleta.2010.11.022
Abstract
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.
24 pages, 2 figures, 1 table
References in corpus (2)
Cited by in corpus (6)
- On Magnetohydrodynamic Gauge Field Theory
- Plane one-dimensional MHD flows: symmetries and conservation laws
- Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations
- Complete classification of stationary flows with constant total pressure of ideal incompressible infinitely conducting fluid
- Godbillon-Vey Helicity and Magnetic Helicity in Magnetohydrodynamics
- Action Principles and Conservation Laws for Chew-Goldberger-Low Anisotropic Plasmas