Open AccessAn exact solution for the dispersive Alfven switch‐on shock
Author(s) -
Hamilton R. L.,
Wu C. C.
Publication year - 2003
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2002ja009653
Subject(s) - shock (circulatory) , physics , exact solutions in general relativity , shock wave , planar , nonlinear system , dispersion (optics) , mechanics , moving shock , classical mechanics , mathematical analysis , optics , quantum mechanics , mathematics , computer science , medicine , computer graphics (images)
An exact solution for the dispersive Alfven switch‐on shock is found in the case of weak nonlinearity, weak dispersion, and weak damping. Two singular and apparently nonphysical solutions are found as well. The switch‐on shock solution is shown to reduce, in the appropriate limits, to two documented special cases of the shock: one case being a description of the planar shock without dispersion and the other being an asymptotic description of the circularly polarized wave standing upstream from the shock in the dispersive case. The solution developed here provides the complete shock structure for either case. This exact solution may serve as a convenient basis for an analytical study of the stability of dispersive switch‐on shocks.