Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation

We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.Comment: 29 pp., 4 figures, 44 reference

Chaos in magnetospheric radio emissions

A three-wave model of auroral radio emissions near the electron plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can occur in the nonlinear evolution of this three-wave process in the magnetosphere. In particular, two types of intermittency, due to either local or global bifurcations, can be observed. We analyze the type-I Pomeau-Manneville intermittency, arising from a saddle-node bifurcation, and the crisis-induced intermittency, arising from an interior crisis associated with a global bifurcation. Examples of time series, power spectrum, phase-space trajectory for both types of intermittency are presented through computer simulations. The degree of chaoticity of this three-wave process is characterized by calculating the maximum Lyapunov exponent. We suggest that the intermit-tent phenomena discussed in this paper may be observed in the temporal signal of magnetospheric radio emissions

A novel type of intermittency in a nonlinear dynamo in a compressible flow

The transition to intermittent mean--field dynamos is studied using numerical simulations of isotropic magnetohydrodynamic turbulence driven by a helical flow. The low-Prandtl number regime is investigated by keeping the kinematic viscosity fixed while the magnetic diffusivity is varied. Just below the critical parameter value for the onset of dynamo action, a transient mean--field with low magnetic energy is observed. After the transition to a sustained dynamo, the system is shown to evolve through different types of intermittency until a large--scale coherent field with small--scale turbulent fluctuations is formed. Prior to this coherent field stage, a new type of intermittency is detected, where the magnetic field randomly alternates between phases of coherent and incoherent large--scale spatial structures. The relevance of these findings to the understanding of the physics of mean--field dynamo and the physical mechanisms behind intermittent behavior observed in stellar magnetic field variability are discussed.Comment: 19 pages, 13 figure

Nonintegrable Interaction of Ion-Acoustic and Electromagnetic Waves in a Plasma

In this paper we re-examine the one-dimensional interaction of electromagnetic and ion acoustic waves in a plasma. Our model is similar to one solved by Rao et al. (Phys. Fluids, vol. 26, 2488 (1983)) under a number of analytical approximations. Here we perform a numerical investigation to examine the stability of the model. We find that for slightly over dense plasmas, the propagation of stable solitary modes can occur in an adiabatic regime where the ion acoustic electric field potential is enslaved to the electromagnetic field of a laser. But if the laser intensity or plasma density increases or the laser frequency decreases, the adiabatic regime loses stability via a transition to chaos. New asymptotic states are attained when the adiabatic regime no longer exists. In these new states, the plasma becomes rarefied, and the laser field tends to behave like a vacuum field.Comment: 19 pages, REVTeX, 6 ps figures, accepted for publication in Phys. Rev.

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

Intermittent chaos driven by nonlinear Alfvén waves

International audienceWe investigate the relevance of chaotic saddles and unstable periodic orbits at the onset of intermittent chaos in the phase dynamics of nonlinear Alfvén waves by using the Kuramoto-Sivashinsky (KS) equation as a model for phase dynamics. We focus on the role of nonattracting chaotic solutions of the KS equation, known as chaotic saddles, in the transition from weak chaos to strong chaos via an interior crisis and show how two of these unstable chaotic saddles can interact to produce the plasma intermittency observed in the strongly chaotic regimes. The dynamical systems approach discussed in this work can lead to a better understanding of the mechanisms responsible for the phenomena of intermittency in space plasmas

A model of CP Violation from Extra Dimension

We construct a realistic model of CP violation in which CP is broken in the process of dimensional reduction and orbifold compactification from a five dimensional theories with $SU(3)\times SU(3) \times SU(3)$ gauge symmetry. CP violation is a result of the Hosotani type gauge configuration in the higher dimension.Comment: 5 page

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

International audienceThe chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed

Chaos in magnetospheric radio emissions

A three-wave model of auroral radio emissions near the electron plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can occur in the nonlinear evolution of this three-wave process in the magnetosphere. In particular, two types of intermittency, due to either local or global bifurcations, can be observed. We analyze the type-I Pomeau-Manneville intermittency, arising from a saddle-node bifurcation, and the crisis-induced intermittency, arising from an interior crisis associated with a global bifurcation. Examples of time series, power spectrum, phase-space trajectory for both types of intermittency are presented through computer simulations. The degree of chaoticity of this three-wave process is characterized by calculating the maximum Lyapunov exponent. We suggest that the intermit-tent phenomena discussed in this paper may be observed in the temporal signal of magnetospheric radio emissions

Localized structures of electromagnetic waves in hot electron-positronplasmas

The dynamics of relativistically strong electromagnetic (EM) wave propagation in hot electron-positron plasma is investigated. The possibility of finding localized stationary structures of EM waves is explored. It is shown that under certain conditions the EM wave forms a stable localized soliton-like structures where plasma is completely expelled from the region of EM field location.Comment: 14 pages, LaTeX, 1 figure can be obtained upon request through email to [email protected]