Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves

Journal Article · Sat Jul 20 04:00:00 EDT 1996 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.51408· OSTI ID:21163499

Webb, G M; Brio, M; Zank, G P ^[1]

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1. Lunar and Planetary Lab., University of Arizona, Tucson, Arizona (United States)

A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in {beta}{approx}1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a{sub g}{sup 2}=V{sub A}{sup 2} where a{sub g} is the gas sound speed and V{sub A} is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation.

• OSTI ID: 21163499
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 382; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALFVEN WAVES
CONSERVATION LAWS
HAMILTONIANS
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
MAGNETOACOUSTIC WAVES
MAGNETOHYDRODYNAMICS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PERIODICITY
PLASMA
PLASMA WAVES
SOUND WAVES
SYMMETRY
TRAVELLING WAVES
VARIATIONAL METHODS
VELOCITY
WAVE PROPAGATION