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The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas

Topics:
QA

Publisher: Cambridge University Press

Year: 2001

OAI identifier:
oai:wrap.warwick.ac.uk:822

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Warwick Research Archives Portal Repository

- (1980). A connection between nonlinear evolution equations and ordinary differential equations of p-type I.
- (2000). A weak turbulence theory for incompressible magnetohydrodynamics.
- (1983). Anisotropy in MHD turbulence due to a mean magnetic J.Plasma Phys.
- (1979). Asymptotic properties of Burgers turbulence.
- (1990). Complex singularities and the Riemann surface for the Burgers equation. In: Nonlinear Physics
- (1994). Dealing with the singularities of analytic functions. In: An Introduction to
- (1998). Density probability distribution in onedimensional polytropic gas dynamics.
- (1998). Direct numerical testing of stationary shock model with low Mach number shock observations.
- (1988). Hamiltonian structures for systems of hyperbolic conservation laws.
- (1991). Integrability, What is integrability? In: Nonlinear Dynamics
- (1981). Intermittency in nonlinear dynamics and singularities at complex times.
- (1991). Intermittent turbulence in the solar wind.
- (1990). Introduction a l'Analyse Complexe.
- (1983). L' equation de Burgers d eterministe et statistique.
- (1986). Le test de Painlev e. In:
- (1993). Magnetic in starformingregions:observations.In:ProtostarsandPlanetsIII
- (1999). Magnetohydrodynamic turbulence in the solar wind.
- (1939). Mathematical examples illustrating relations occurring in the theory of turbulent uid motion.
- (1999). Mechanisms of injection and dissipation of energy and their relation to the dynamics of the interstellar medium. In: New Perspectives on the Interstellar Medium.
- (1989). Meromorphic integrals of two nonintegrable systems. In: Non Linear Dynamics
- (1970). Model equations for magnetohydrodynamic turbulence. A gas dynamics analogy.
- (1994). Non-Gaussian probability distributions of solar wind uctuations.
- (1968). Numerical experiments on a model system for magnetohydrodynamic turbulence.
- (1951). On a quasi-linear parabolic equation occurring in aerodynamics.
- (1997). On the decay of Burgers turbulence.
- (1973). Ordinary Differential Equations.
- (1990). Partially Integrable Evolution Equations in Physics.
- (1991). Physics of the Inner Heliosphere II: Particles, Waves and Turbulence.
- (1984). Pole condensation and the Riemann surface associated with a shock in Burgers'
- (1980). Properties of magnetohydrodynamic turbulence in the solar wind.
- (1986). Propri et es locales et singularit es complexes en dynamique non lin ea re. In:
- (1986). Relaxation and magnetic reconnection in plasmas.
- (1979). Remarques sur un mod ele unidimensionnel pour la turbulence magn etohydrodynamique.
- (1981). Resistivity and energy ow in a plasma undergoing magnetic line reconnection.
- (1997). Scaling of anisotropic spectra due to the weak interaction of shear-Alfv en wave packets.
- (1998). Shocks and antishocks in the MHD{Thomas model. In:
- (1988). Singularity clustering in the Duf oscillator.
- (1998). Solar are statistics with a one-dimensional MHD model. Solar Phys.
- (1982). Solar Magnetohydrodynamics.
- (1994). Spontaneous Current Sheets in Magnetic Fields.
- (1992). The equations of reduced magnetohydrodynamics.
- (1996). The heating and activity of the solar corona: boundary shearing of an initially homogeneous magnetic
- (1974). The Nonlinear Diffusion Equation.
- (1986). The Painlev e analysis on the Burgers'
- (1983). The Painlev e property for partial differential equations.
- (1950). The partial differential equation ut + uux = uxx.
- (1983). Tracing complex singularities with spectral methods.
- (1998). Weakly compressible magnetohydrodynamic turbulence in the solar wind and the interstellar medium.

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